# @yuktimittal

##### 34 karma IIM
###### CATdoubts in permutation & combination
The probability of the angle being acute is 1/4 only not 3/4.
Why dont you refer the below mentioned link ?

Geometric Probabilities from Interactive Mathematics Miscellany and Puzzles

Sayonara

ps- thanks, coz the link u hv given is vry useful.
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###### CATQuant by Arun Sharma
thanks so much shanks4mba, wintersanshul

I got another doubt from this problem

ten tickets numbered 1,2,3..,10. Six tickets are selected at random one at a time with replacement. The probability that the largest number appearing on the selected ticket is 7 is

Ans is (7^6)-(6^6)/10^6

with explanation plsss

no. of ways 4 nt selecting 8, 9 and 10 =7 /10.
as we have to select 6 tickets thus no. of ways = 7^6/10^6
bt in the selected 6 tickets the highest no can also be 6 (1,2,3,4,5,6 numbered ticket) thus we subtract the cases of highest no.on any of the 6 tickets being 6 which is not selecting 7,8,9 and 10 = 6^6/10^6
therefore the ans. is (7^6)-(6^6)/10^6
###### CATdoubts in permutation & combination
Puys help me out in these 3 Qs
1.Rallis has got the order from Switzerland to export 80, 96, 64 and 128 bottle of Rose, Orange, green and Baidam syrup respectively. He wants to send consignment in minimum boxes of capacity of 64 bottles, however boxes should have equal number of different variety of bottles. For the above purpose he can add more bottle. Again boxes can be kept empty by 1 bottle only so as to prevent breakage. How many Baidam syrup cant be sent?
10,11,12,15

2.Aryan and Nandini are siblings. They participated in two different competition i.e. swimming and wrestling respectively. Aryan participated in swimming and Nandini in wrestling. Both were awarded rank between 1 to 50 (including 1 and 50). What is the probability that difference between their ranks is not more than 10 rank?
Options :9/25 ,17/40,4/10,3/10

3.Points A, B and C are randomly selected on the circumference of a circle. What is the probability of angle ABC being acute?
Options :1/4,3/4,1/2,3/5

2nd question:total cases 4 d ranks will b 50 *50
n d cases where d differences b/w thr ranks is not more than 10 will be 940( to calculate 940 consider ranks indivisually for eg. if aryan's rank is 1 nandini can hv 11 ranks;aryans rank is 2 den nandini can hv 12 ranks dis goes on increasin by 1 till aryans rank is 11 after dis if aryan's rank is in b/w 11 to 40 den nandini can hv 21 ranks 4 eachn from aryans rank 40 nandini will hv 20 ranks dis goes on decreasin till arans rank is 50)
from d above u get 940
last step: 940/(50*50) ans is approximately 9/25

3rd question: draw a circle n construct any chord AB nw consider d point diametrically opp. to A(call it X) you will see that as you chose a pt. C b/w
b and x the angle abc become obtuse. thus the ans will be atleast 1/2. if c is taken b/w A and B den also d angle will be acute thus some value has to be added to 1/2, nw this value depends on distance b/w A n B so we take the mean of 2 extreme values of B ( i.e. closest and farthest from A) closest will be very close to zero and farthest can be a point very close to X thus (0+pr)/2 thus probablity becomes 1/2+ = 1/2 +1/4 = 3/4
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###### CATdoubts in permutation & combination
Puys help me out in these 3 Qs
1.Rallis has got the order from Switzerland to export 80, 96, 64 and 128 bottle of Rose, Orange, green and Baidam syrup respectively. He wants to send consignment in minimum boxes of capacity of 64 bottles, however boxes should have equal number of different variety of bottles. For the above purpose he can add more bottle. Again boxes can be kept empty by 1 bottle only so as to prevent breakage. How many Baidam syrup cant be sent?
10,11,12,15

2.Aryan and Nandini are siblings. They participated in two different competition i.e. swimming and wrestling respectively. Aryan participated in swimming and Nandini in wrestling. Both were awarded rank between 1 to 50 (including 1 and 50). What is the probability that difference between their ranks is not more than 10 rank?
Options :9/25 ,17/40,4/10,3/10

3.Points A, B and C are randomly selected on the circumference of a circle. What is the probability of angle ABC being acute?
Options :1/4,3/4,1/2,3/5

ans 2. 9/25
ans 3. 3/4
r the anwers right?
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###### CATdoubts in permutation & combination
If the letters of the word REGULATIONS are arranged at random, the chance that there will be exactly four letters between R and E is
1. 1/3
2. 2/7
3. 6/55
4. 7/55

explain too

ans. 3. 6/55
total positons that r and e can take when placed randomly= 11*10
no. of positions that r and e can take when there are exctly 4 letters between them =12

so 12/(11*10)= 6/55
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###### CATdoubts in permutation & combination
its given in the statement u quoted that the answer is 84...

thnx dint see dat in a hurry plus i dint do d last step
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###### CATdoubts in permutation & combination
visionIIM-ACL Says
my take: option 4 ( 45 * 3^8 )

hey if the question was that any one of the boxes contains 2 balls,then 4*45*3^8 would b the right ans..
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###### CATdoubts in permutation & combination
Q) There are 6 points in a circle, 5 events occur at 5 of these points. What are the total number of ways such that no two successive events occur at the adjoining points.

36 are the no of ways in which the event occur at successive positions
so total 120 minus 36 will give u the ans
120 - 36 = 84

This is a question few days, could not get the solution, can someone please elucidate.

m gettin d same ans. 84
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###### CATdoubts in permutation & combination
Hi puys, Crack them:

Q1) Out of a pack of 52 cards one is lost; from the remainder of the pack, two cards are drawn and are found to be spades. Find the chances of the missing card be spade:

a) 11/50
b) 11/49
c) 10/49
d) 25/34

Q2) If the integers 'm' and 'n' are chosen at random from 1 to 100, then the probability that the number of the form 7^m + 7^n is divisible by 5 is

a) 1/4
b) 1/2
c) 1/16
d) 1/8

Q3) Two small squares on a chess board are chosen at random. Find the probability they have a common side

a) 1/12
b) 1/18
c) 2/15
d) 3/14

Q4) A bag contains 5 black and 3 red balls. A ball is taken out of the bag and is not returned to it. If this process is repeated 3 times, then what is the probability of drawing a black ball in the next draw of a ball?

a) 0.7
b) 0.625
c) 0.1
d) None of these

d 2nd question can also be done by cyclicity of 7.. dats is
7^1=7
7^2=49
7^3=343
7^4=2401

so we hv 7,9,3,1 which will repeat.. so till 100 thr will b 25 such sets n for m=1 n=3(7+343=350).. thr will b a total of 25 values for n for 1 value of m and if m=2 den n=4(49+2401) dis will also giv us 25 values
so d probability becomes (25/100)*(25/100)=1/16
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###### CATdoubts in permutation & combination
arijitprepares Says
Hi puys I am really in a soup with this problem...Can anyone please provide me with some reasoning...Please help me puys, stuck for 3-4 days with this...

it wil b (p-2)c3
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