Question

There are 5 women and 9 men signed up to join a swing dance dass, In how many ways can the instructor choose 6 of the people to join if more than 3 must bemen?0х5 ?

Answer 1

There are p=5 women and q=9 men.

6 people have to be chosen and out of it more than 3 must be men.

So, the people can be chosen as:

• 4 men and 2women

or

• 5 men and 1 woman

or

• 6 men and no woman.

So, the number of ways of choosing 6 people if more than 3 must be men is,

`\begin{gathered} N=n(4\text{ men and 2 woman)+n(5 men and 1 woman)+n(6 men)} \\ =^qC_4*^pC_2+^qC_5*^pC_1+^qC_6 \\ =^9C_4*^5C_2+^9C_5*^5C_1+^9C_6 \\ =126*10+126*5+84 \\ =1260+630+84 \\ =1974 \end{gathered}`

Therefore, there are 1974 ways of choosing 6 people if more than 3 must be men.