how many 7 digit numbers are there having the digit 3 three times and 5 four times
7!/(3!*5!)
3^3 *5^5
77
35
@mailtoankit said:kaise kiya ?
2^2 * 3^3 * 5^3 * 7^5
Divisors of the form 4n+1 :
Take out 2^2
The no is now = 3^3 * 5^3 * 7^5
Now, the no gives remainder 1 when divided by 4
= (-1)^a * (1)^b * (-1)^c
b can be anything from 0-3, hence 4 choices
a+c = even = 12 ways
Total = 12*4 = 48
Hope I'm not making a mistake //
@aashu25 said:I have this another problem :Two people A and B from P and Q (distance=D) at the same time towards each other. They meer at a point R, which is a distance 0.4D from P. They continue to move to and fro between the two points. Find the distance from point P at which the 4th meeting takes place.(Please share your approach for different meetings in these problems like if they would have met for the 5th time . . then what would have been done ... The common approach is needed)a. 0.8Db. 0.4Dc. 0.6Dd. 0.3D
A.
divide the line into 5 parts (since their speeds are 2:3 )and... move them to and fro accordingly.
P(A)3rd______.________.1st/5th_________._______2nd/4th._______Q(B)
so 1st meet at 0.2D from P, next will be 0.8D from P , next will be P. and 4th will be 0.8 D.
Fifth meet ... 0.2D from P.
correct me if i am wrong.
divide the line into 5 parts (since their speeds are 2:3 )and... move them to and fro accordingly.
P(A)3rd______.________.1st/5th_________._______2nd/4th._______Q(B)
so 1st meet at 0.2D from P, next will be 0.8D from P , next will be P. and 4th will be 0.8 D.
Fifth meet ... 0.2D from P.
correct me if i am wrong.
@ScareCrow28 said:2^2 * 3^3 * 5^3 * 7^5Divisors of the form 4n+1 :Take out 2^2The no is now = 3^3 * 5^3 * 7^5Now, the no gives remainder 1 when divided by 4 = (-1)^a * (1)^b * (-1)^cb can be anything from 0-3, hence 4 choicesa+c = even = 12 waysTotal = 12*4 = 48Hope I'm not making a mistake ( I feel I am making one here ) ..
from last 4th line plz elaborate more
@raopradeep said:from last 4th line plz elaborate more
See, the remainder is 1 when divided by 4.
And divisors will be of the form 3^a * 5^b * 7^c
3^a mod 4 = (-1)^a
5^b mod 4 = (1)^b
7^c mod 4 = (-1)^c
Hence, remainder = (-1)^a * (1)^b * (-1)^c ---> This has to be 1
So (-1)^(a+c) * (1)^b = 1
=> b can be anything and a+c = even
anita has 3 cards and 7 books of her interest . of these she would not like to borrow di book unless quant book is also borrowed . in how many ways she can borrow 3 books
15
20
25
30
@ChirpiBird said:A.divide the line into 5 parts (since their speeds are 2:3 )and... move them to and fro accordingly.P(A)3rd______.________.1st/5th_________._______2nd/4th._______Q(B)so 1st meet at 0.2D from P, next will be 0.8D from P , next will be P. and 4th will be 0.8 D.Fifth meet ... 0.2D from P.correct me if i am wrong.
method is correct but a simpler approach will be
Look they meet at .4D from P so the ratio of their speeds will be 2:3..
Now you want to find the distance from P when they meet for the 4th time..
From 2nd meet onwards they will together cover a distance of 2D. so for 4th meet they wil cover an additional distance of 6D..
From this 6D A will cover 6d*(2/5) = 1.4D.
From the meeting point A will travel an additional 1.4D which is .8D from P..
Hope this help :)
Look they meet at .4D from P so the ratio of their speeds will be 2:3..
Now you want to find the distance from P when they meet for the 4th time..
From 2nd meet onwards they will together cover a distance of 2D. so for 4th meet they wil cover an additional distance of 6D..
From this 6D A will cover 6d*(2/5) = 1.4D.
From the meeting point A will travel an additional 1.4D which is .8D from P..
Hope this help :)
@ChirpiBird said:A.divide the line into 5 parts (since their speeds are 2:3 )and... move them to and fro accordingly.P(A)3rd______.________.1st/5th_________._______2nd/4th._______Q(B)so 1st meet at 0.2D from P, next will be 0.8D from P , next will be P. and 4th will be 0.8 D.Fifth meet ... 0.2D from P.correct me if i am wrong.
method is correct but a simpler approach will be
Look they meet at .4D from P so the ratio of their speeds will be 2:3..
Now you want to find the distance from P when they meet for the 4th time..
From 2nd meet onwards they will together cover a distance of 2D. so for 4th meet they wil cover an additional distance of 6D..
From this 6D A will cover 6d*(2/5) = 1.4D.
From the meeting point A will travel an additional 1.4D which is .8D from P..
Hope this help :)
Look they meet at .4D from P so the ratio of their speeds will be 2:3..
Now you want to find the distance from P when they meet for the 4th time..
From 2nd meet onwards they will together cover a distance of 2D. so for 4th meet they wil cover an additional distance of 6D..
From this 6D A will cover 6d*(2/5) = 1.4D.
From the meeting point A will travel an additional 1.4D which is .8D from P..
Hope this help :)
@raopradeep said:how many 7 digit numbers are there having the digit 3 three times and 5 four times7!/(3!*5!)3^3 *5^57735
7!/(3!*4!)=35
:neutral:
@raopradeep said:anita has 3 cards and 7 books of her interest . of these she would not like to borrow di book unless quant book is also borrowed . in how many ways she can borrow 3 books15202530
25?
Case 1) when she needs to borrow DI book so she also has to borrow the Quant book. so this can be done in 1 way. The third book can be chosen in (7-2)c1= 5 ways
Case 2)when she doesnt want to borrow DI book. So she has to select 3 books from a possible 6 choices. Thus 6c3=20
so total selection is 25.
If i am wrong kindly correct me
Case 1) when she needs to borrow DI book so she also has to borrow the Quant book. so this can be done in 1 way. The third book can be chosen in (7-2)c1= 5 ways
Case 2)when she doesnt want to borrow DI book. So she has to select 3 books from a possible 6 choices. Thus 6c3=20
so total selection is 25.
If i am wrong kindly correct me
@raopradeep said:anita has 3 cards and 7 books of her interest . of these she would not like to borrow di book unless quant book is also borrowed . in how many ways she can borrow 3 books15202530
25 ?
5c3 + 5c2 + 5c1 = 25
@raopradeep said:anita has 3 cards and 7 books of her interest . of these she would not like to borrow di book unless quant book is also borrowed . in how many ways she can borrow 3 books15202530
Can you please look again at this question? Looks incorrect to me.
:neutral:
@raopradeep said:@ScareCrow28 a+c=12 kaise aaya ?
a+c = 12 nai aya...but there are 12 cases where a+c = even!
Put a=0-3 and find satisfying values of c..you will find there are 12 cases
@vijay_chandola sahi hai bhai i think @mailtoankit ne oa daala hai and thats right one
got confused in 7!/(3!*5!) thanks bro :)
@vijay_chandola said:7!/(3!*4!)=35
got confused in 7!/(3!*5!) thanks bro :)@mailtoankit said:25 ?5c3 + 5c2 + 5c1 = 25
Bhai is there any relation between the cards and books ? :embarrassed:
I didn't get it.
:neutral:
@aashu25 said:The metro service has a train going from Mumbai to Pune and Pune to Mumbai every hour, the first one at 6 am. The trip from one city to other takes 4.5 hours, and all trains travel at same speed. How many trains will you pass while going from Mumbai to Pune if you start at 12 noon ?(Please share your approach)a.7b.8c.9d.13
boarding time _______reaching time
6=========10:30
7=========11:30
8=========12:30 (+ pune starts a train at 12:00)
9=========1:30(+ pune starts a train at 1:00)
10=========2:30 + pune starts a train at 2:00
11=========3:30 +pune starts a train at 3:00
12.. (u boarded this) .....u'll reach at 4:30 (+ pune starts a train at 12:00)
so total 9 trains.. 12,12:30, 1, 1;30,2, 2:30, 3, 3:30 and 4.
6=========10:30
7=========11:30
8=========12:30 (+ pune starts a train at 12:00)
9=========1:30(+ pune starts a train at 1:00)
10=========2:30 + pune starts a train at 2:00
11=========3:30 +pune starts a train at 3:00
12.. (u boarded this) .....u'll reach at 4:30 (+ pune starts a train at 12:00)
so total 9 trains.. 12,12:30, 1, 1;30,2, 2:30, 3, 3:30 and 4.