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?

Question

asked Apr 17, 2023 154k views

1 Answer

Tommy Nicholas · Answer 1 · 2023-04-22T14:25:53+0000

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