Question

How many ways can a team of 4 engineers be selected from a group of 7 engineers

Answer 1

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 $^{n}C_{r}=\frac{n!}{r!*(n-r)!}$, where

• n represents the total number of items
• r represents the number of items being chosen at a time.

The order is not important in this problem, so we can use the  combination $^{n}C_{r}$

∵ The group has 7 engineers

∴ n = 7

∵ The team has 4 engineers

∴ r = 4

∵  $^{n}C_{r}=\frac{n!}{r!*(n-r)!}$

∴  $^{7}C_{4}=\frac{7!}{4!*(7-4)!}$

∴  $^{7}C_{4}=\frac{7!}{4!*(3)!}$

∵ 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1

∵ 4! = 4 × 3 × 2 × 1

∵ 3! = 3 × 2 × 1

∴ $^{7}C_{4}$ = $\frac{(7)(6)(5)(4)(3)(2)(1)}{(4)(3)(2)(1).(3)(2)(1)}$

∴ $^{7}C_{4}$  = 35

There are 35 ways a team of 4 engineers can be selected from a group of 7 engineers