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  • In how many ways can a committee of 3 people be selected from a group of 6 men and 4 women, if the committee must include at least 1 woman?  Optio

In how many ways can a committee of 3 people be selected from a group of 6 men and 4 women, if the committee must include at least 1 woman?

 

Option: 1

100


Option: 2

120


Option: 3

150


Option: 4

200


Answers (1)

best_answer

The number of ways to select 1 woman from the 4 available women is 4 C_1=4
The number of ways to select 2 men from the 6 available men is 6 C_2=15Therefore, the total number of ways to form the committee with 1 woman and 2 men is 4 \times 15=60 The number of ways to select 2 women from the 4 available women is 4 C_2=6 The number of ways to select 1 man from the 6 available men is 6 C_1=6 
Therefore, the total number of ways to form the committee with 2 women and 1 man is 6 \times 6=36 The number of ways to select 3 women from the 4 available women is 4 C_3=4 Now, we can add up the total number of ways from each scenario to get the final answer:  60+36+4=100 

Therefore, there are 100 different ways to select a committee of 3 people from a group of 6 men and 4 women, where the committee must include at least 1 woman.

 

 

Posted by

Suraj Bhandari

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