A committee of 6 members is to be selected from a group of 8 men and 6 women in such as way that at least 3 men are there in the committee. In how many different ways can it be done ?
A committee of 6 members is to be selected from a group of 8 men and 6 women in such as way that at least 3 men are there in the committee. In how many different ways can it be done ?
1). 2506
2). 2534
3). 1120
4). 1050
2 answers
There are a total of 8 men and 6 women.
Number of ways in which the committee has exactly 3 men is $^8C_3 \times ^6C_3 = 1120$
Number of ways in which the committee has exactly 4 men is $^8C_4 \times ^6C_2 = 1050$
Number of ways in which the committee has exactly 5 men is $^8C_5 \times ^6C_1 = 336$
Number of ways in which the committee has exactly 6 men is $^8C_6 \times ^6C_0 = 28$
Hence, the total is $1120 + 1050 + 336 + 28 = 2534$
There are a total of 8 men and 6 women.
Number of ways in which the committee has exactly 3 men is $^8C_3 \times ^6C_3 = 1120$
Number of ways in which the committee has exactly 4 men is $^8C_4 \times ^6C_2 = 1050$
Number of ways in which the committee has exactly 5 men is $^8C_5 \times ^6C_1 = 336$
Number of ways in which the committee has exactly 6 men is $^8C_6 \times ^6C_0 = 28$
Hence, the total is $1120 + 1050 + 336 + 28 = 2534$
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