Alan

Check the previous answer at http://web2.0calc.com/questions/whats-8-17-a-m-9houres-50-minutes 

"Given that integers x and y satisfying the equation 3x+5y=1. If S=x-y and S>2007, find the least possible value of S."

x = S + y   so  3x + 5y = 1 can be written as  3(S + y) + 5y = 1

Rearrange to find y in terms of S:     y = (1 - 3S)/8  This must be an integer so try values of S from 2008 onwards:

S           y

2008    -752.875    no

2009   -753.25       no

2010   -753.625     no

2011   -754            yes

So  S = 2011

Here's the solution to (a):

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If people are to learn from this site NinjaAnswer they would generally appreciate an explanation of how the answer is obtained!

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Note that after choosing one of the 12 black shoes, say, there are only 6 black shoes of the opposite parity left.

p(black pair) = (12/22)*(6/21) → 72/462

p(brown pair) = (6/22)*(3/21) → 18/462

p(grey pair) = (4/22)*(2/21) → 8/462

p(matching pair) = (72 + 18 + 8)/462 → 98/462 → 7/33

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p(at least 1 boy and at least 1 girl) = 1 - p(no boys) - p(no girls)

 → 1 - 2*ncr(20,4)(1/2)²⁰

p = nCr(7,2)*(3/4)²*(1/4)^(7-2) → 0.01154

Note:  nCr(7,2) = 7!/(2!*5!) = 7*6/2 = 21

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I get the following for (a):

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Just keep pressing the square root button \(\sqrt x\)  fourth row, fourth column.

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