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## Comment on

Odd or Even## Say there are 5 matching

though not sure

## Perfect!

Perfect!

P(no matching pair) = P(select ANY sock as 1st selection AND select a NON-MATCHING sock as 2nd selection)

= P(select ANY sock as 1st selection) x P(select a NON-MATCHING sock as 2nd selection)

= 1 x 8/9

= 8/9

ASIDE: For others following along, the second probability is 8/9, because once we've selected the 1st sock, there are 9 socks remaining. Of these 9 socks, 1 sock matches the 1st sock selected, and the other 8 socks are NOT a match.

## Hi Brent,

If it were a counting question asking how many ways we can select two non matching sock, how would we go about it using FCP ?

## Here's one approach:

Here's one approach:

First off, let's say that, for each pair of matching socks, we have a left sock and a right sock.

STAGE 1: Choose 2 colors

There are 5 colors. Since the order in which we select the socks does not matter, we can use combinations.

We can select 2 colors from 5 colors in 5C2 ways (10 ways)

ASIDE: Now, from each color, we'll select either a left sock or a right sock

STAGE 2: From one color, choose a left or right sock

This can be accomplished in 2 ways

STAGE 3: From the other color, choose a left or right sock

This can be accomplished in 2 ways

TOTAL number of ways to select 2 NON-MATCHING socks = (10)(2)(2)

= 40

For "fun", let's also determine the denominator.

TOTAL number of ways to select ANY 2 socks = 10C2 = 45

So, P(no matching pair) = 40/45 = 8/9

Cheers,

Brent

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