Question

Student Painters, which specializes in painting the exterior of residential buildings, has ten people available to be organized into six-person and four-person teams. (a) In how many ways can the six-person team be formed? ways (b) In how many ways can the four-person team be formed? ways (c) In how many ways can the company organize the available people into six- or four-person teams? ways

Answer 1

Using the combination formula, it is found that:

a) A six-person team can be formed in 210 ways.

b) A four-person team can be formed in 210 ways.

c) There are 420 ways.

What is the combination formula?

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Item a:

Teams of 6 from a set of 10, hence:

$C_{10,6} = \frac{10!}{6!4!} = 210$

A six-person team can be formed in 210 ways.

Item b:

Teams of 4 from a set of 10, hence:

$C_{10,4} = \frac{10!}{4!6!} = 210$

A four-person team can be formed in 210 ways.

Item c:

Adding items a and b:

210 + 210 = 420.

There are 420 ways.

You can learn more about the combination formula at https://brainly.com/question/25821700