Please show all steps and use the same numbers shown in the problem so that I ca

Question

Please show all steps and use the same numbers shown in the problem so that I can follow along easily. Thank you.

5. There are 150 socks in a bin: 30 blue, 10 pink, 20 green, 40 black, and 50 white. 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 (same 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. A. 30 B. 66 C. 350 D. 705 E. 846

Explanation / Answer

For m, we have

We need minimum number of socks that ensure that he has at least one matching pair. Taking into account the worst case which is

1 socks from each color which means 5 different socks, hence the 6th one accounts for value of m.

Therefore, m = 6.

For M, we have

We need minimum number of socks that ensure that he has at least one sock of each color. Taking into account the worst case which is

50 socks of white, 40 of black, 30 of blue, 20 of green which is 140, hence the 141th of pink is which one accounts for value of M.

Therefore, M = 141.

Hence, product of m and M is = 6*141= Option E (846).

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