Answer:
There are 35 ways a team of 4 engineers can be selected from a group of 7 engineers ⇒ b
Step-by-step explanation:
Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.
To calculate combinations, we will use the formula [tex]^{n}C_{r}=\frac{n!}{r!*(n-r)!}[/tex], where
The order is not important in this problem, so we can use the combination [tex]^{n}C_{r}[/tex]
∵ The group has 7 engineers
∴ n = 7
∵ The team has 4 engineers
∴ r = 4
∵ [tex]^{n}C_{r}=\frac{n!}{r!*(n-r)!}[/tex]
∴ [tex]^{7}C_{4}=\frac{7!}{4!*(7-4)!}[/tex]
∴ [tex]^{7}C_{4}=\frac{7!}{4!*(3)!}[/tex]
∵ 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
∵ 4! = 4 × 3 × 2 × 1
∵ 3! = 3 × 2 × 1
∴ [tex]^{7}C_{4}[/tex] = [tex]\frac{(7)(6)(5)(4)(3)(2)(1)}{(4)(3)(2)(1).(3)(2)(1)}[/tex]
∴ [tex]^{7}C_{4}[/tex] = 35
There are 35 ways a team of 4 engineers can be selected from a group of 7 engineers
