From 7 women and 9 men a committee of 5 is to be formed. How many ways the
selection can be made if
(i) at least one woman must be on the committee
(ii) atleast one woman and one man must be on the committee
please help me fast
selection can be made if
(i) at least one woman must be on the committee
(ii) atleast one woman and one man must be on the committee
please help me fast
Answers & Comments
Step-by-step explanation:
We can use the formula for combinations to find the number of ways to form a committee of 5 people from 7 women and 9 men:
(rn)=r!(n−r)!n!
where n is the total number of people, and r is the number of people to be selected.
(i) To find the number of ways to form a committee of 5 people with at least one woman, we can subtract the number of committees with no women from the total number of committees:
(516)−(59)=4368
Therefore, there are 4368 ways to form a committee of 5 people with at least one woman.
(ii) To find the number of ways to form a committee of 5 people with at least one woman and one man, we can subtract the number of committees with only women or only men from the total number of committees:
(516)−(57)−(59)=4140
Therefore, there are 4140 ways to form a committee of 5 people with at least one woman and one man.
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