SOLUTION: Toni has 10 identical blue socks, 14 identical green socks, and 4 identical red socks in a drawer. She removes socks from the drawer one at a time at random without looking. The le

Question 1198950: Toni has 10 identical blue socks, 14 identical green socks, and 4 identical red socks in a drawer. She removes socks from the drawer one at a time at random without looking. The least number of socks that Toni needs to pull out to be sure of having 4 pairs of the same colour is:
a) 8
b) 15
c) 16
d) 19
e) 22

Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.
Toni has 10 identical blue socks, 14 identical green socks, and 4 identical red socks in a drawer.
She removes socks from the drawer one at a time at random without looking.
The least number of socks that Toni needs to pull out to be sure of having 4 pairs of the same colour is:
a) 8
b) 15
c) 16
d) 19
e) 22
~~~~~~~~~~~~~~~~~

In the worst case scenario, Toni will pull out 4 identical red socks, 7 identical blue socks and 7 identical green socks,
but still will not have 4 pairs of the same color.

Notice that 4 + 7 + 7 = 18 socks.

But then, had Toni pull out anyone of remaining socks from the drawer,
this 19-th sock will create four pairs of identical socks, either blue or green.

Therefore, the least number of socks that Toni needs to pull out to be sure of having 4 pairs of the same color is 19.

Solved.

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