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There are 150 socks in a bin: 30 blue, 10 pink, 20 green, 40 black, and 50 white

ID: 3365297 • Letter: T

Question

There are 150 socks in a bin: 30 blue, 10 pink, 20 green, 40 black, and 50 white. Jerry randomly pulls socks out of the drawer, one at a time, and does not replace them. Let m be the minimum number of socks that he would need to pull out to guarantee that he has at least one matching (some color) pair. Let M be the minimum number of socks that he must pull out to guarantee that he has at least one sock of each color. Find the product of m and M. Show the work. There are 150 socks in a bin: 30 blue, 10 pink, 20 green, 40 black, and 50 white. Jerry randomly pulls socks out of the drawer, one at a time, and does not replace them. Let m be the minimum number of socks that he would need to pull out to guarantee that he has at least one matching (some color) pair. Let M be the minimum number of socks that he must pull out to guarantee that he has at least one sock of each color. Find the product of m and M. Show the work. Show the work.

Explanation / Answer

As there are 5 different type of socks hence if we take at least 6 socks ,we can be sure that we have at least one matching (some color) pair , (remember pigeonhole principal)

hence m = 6

min (30.10,20,40,50) = 10

150 -10 =140

hence we can draw maximum 140 socks that socks of all colour are not withdrawn

hence M = 141

m*M = 6*141 = 846