[maildc16]

hello!

I have a doubt regarding Q 76. In the sol it is given that The no. of ways in which the 1st person doesn't pick up his own top-coat is 3. The 2nd person (whose top-coat the 1st one picked)can pick someone else's top-coat in 3 more ways. For the 3rd and 4rth person we have just 1 choice. Thus, in all when none among the 4 pick his/her own top-coat is 9. Thus p = 9*9 = 81.

However how do u know that always the case is 'The 2nd person (whose top-coat the 1st one picked)' is true. If it is not then for the 2nd person there r 2 ways (excluding his own top coat that is not yet picked). Now the 3rd person can also pick in 2 ways, for the 4th person it is just 1 way. So the total ways is 3x2x2x1=12 ways.

Am i right?. Plz explain

[sunit_chotu]

Originally Posted by pratyush_sinha

100 99 85 84..........40 39
98 * 83 * 38 *
97 96 82 81 37 36
95 * 80 * 35 *
94 93 79 78 34 33
92 * 77 * 32 *
91 90 76 75 31 30
89 * 74 * 29 *
88 87 73 72 28 27
86 * 71 * 26 *

Continue the same for another 6 more columns.

The * will be filled with 1-25

The calculation 15 * 5 =75 but the 3 digits at the right handside corner will have to be discounted.

75 -3 =72

thanks

some flaws in ur solution see the red bold figures, they do not satisfy the condition as for eg 82 is less than 96 as well as 83. can u explain this.

[krsh.vik]

I think i have managed to get 72 finally

please see the doc attached

in the doc all a's are > b's
all c's are > b's
all d's > c's
all g's > d's

[sunit_chotu]

Originally Posted by krsh.vik

I think i have managed to get 72 finally

please see the doc attached

in the doc all a's are > b's
all c's are > b's
all d's > c's
all g's > d's

can u put some value in this and check.

[sunit_chotu]

@Aarav its time now to leave office can u please post the solution for today's question. I know there has to be some simpler method than what we have been trying. it is hundred so we could do all this if it would be given 400 students, 20 rows and 20 columns , there has to be some generalization.

[mohit_353]

post deleted

[Aarav]

Originally Posted by sunit_chotu

@Aarav its time now to leave office can u please post the solution for today's question. I know there has to be some simpler method than what we have been trying. it is hundred so we could do all this if it would be given 400 students, 20 rows and 20 columns , there has to be some generalization.

Ya sure, but will do that once back home. Will take around 20/25 minutes to put in the exact words. You can come back and check the solution tomorrow :-)

[mohit_353]

Originally Posted by Aarav

Ya sure, but will do that once back home. Will take around 20/25 minutes to put in the exact words. You can come back and check the solution tomorrow :-)

is the answwer 64 (option d) ????? anybody else ..pls confirm it ..?

[thakurji]

Originally Posted by sunit_chotu

What i did in this question is

let f(x) = a0+a1x+a2x^2 + ............ + a(n-1)*x^(n-1)+an*x^n.

where a0,a1,a2,.............a(n-1),an are coefficient of the expression f(x).

now f(1-x) = a0 + a1*(1-x) + a2(1-x)^2 + ..............+ a(n-1)*(1-x)^(n-1)+ an*(1-x)^n

now, an*(1-x)^n = an*[nC0 - nC1*x^1+................+nCn-1*x^(n-1) - nCn*x^n. (-ve sign as n is odd)

also a(n-1)*(1-x)^(n-1) = a(n-1)*[n-1C0 - n-1C1*x^1+................- n-1Cn-2*x^(n-2) + n-1Cn-1*x^(n-1). (+ve sign as n-1 will be even)

now after adding both f(x)+f(1-x)

= x^n * [an - an] + x^(n-1) * [ n*an+2*a(n-1) ] + all other terms.

now according to the question the degree of f(x) + f(1-x) is atleast two less than the degree of f(x) hence coefficient of x^n and x^(n-1) should be zero.
here coefficient of x^n is always zero.


hence, [ n*an+2*a(n-1) ] = 0

also given that a2 = -a1.
even for degree 3 it should be 3*a3 = -2a2 = 2a1.


now here i am stuck.

@ Aarav bhai ur expert comments required.

What's the exact answer to the above quesn?

[Aarav]

The answer to #79 is (e).

For today's problem it is option (a). Please find attached the DOC for the solution.
This solution is pretty comprehensive and doesn't require any editing as thought earlier.