Question

there are 6 women and 7 men signed up to join a salsa dance class. in how many ways can the instructor choose 5 of the people to join if 4 or more must be men?

Answer 1

Data:

• 6 women

,

• 7 men

,

• Total = 6 + 7 = 13

Steps:

0. We have to calculate the option where we 5 five men only:

Formula:

`C_(n,x)=(7!)/(5!\cdot(7-5)!)=21`

2. Then, we have to make the calculations for the option in which we choose one woman

`C_(n,x)=(7!)/(4!\cdot(7-4)!)=35`

3. We multiply the last result times 6 because that is the number of groups we could make:

`\text{Total}=35\cdot6+21=231`

Answer: 231