Geronimo wrote:
A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed if two of the men refuse to serve together?
(1) 635
(2) 700
(3) 1404
(4) 2620
(5) 3510
Since the committee must have 6 people, there are two cases that meet the given restrictions:
1) The committee has 2 men and 4 women
2) The committee has 3 men and 3 women
1) The committee has 2 men and 4 womenSince the order in which we select the men and women does not matter, we can use COMBINATIONS
We can select 2 men from 8 men in 8C2 ways (=
28 ways)
We can select 4 women from 5 women in 5C4 ways (=
5 ways)
So, the total number of ways to select 2 men and 4 women =
28 x
5 =
1402) The committee has 3 men and 3 womenWe can select 3 men from 8 men in 8C3 ways (=
56 ways)
We can select 3 women from 5 women in 5C3 ways (=
10 ways)
So, the total number of ways to select 2 men and 4 women =
56 x
10 =
560So, the TOTAL number of ways to create the 6-person committee =
140 +
560 =
700Answer: B
Cheers,
Brent
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