Answer to Question #202869 in Statistics and Probability for Max

Question

A box contains 20 coloured balls. There are 5 balls each with the following colours: blue, red, yellow and green. The 5 balls of each colour are numbered from one to five. 4 balls are randomly selected at once.

a)How many ways can 4 balls of the same colour be selected?

b)How many ways can exactly 2 of the 4 balls selected have the same colour?

c)How many ways can the 4 balls selected consist of 2 balls each of two different numbers?

Answer 1

a)

$$4\dbinom{5}{4}\dbinom{15}{0}=4(5)=20$$

20 ways

b)

Exactly two blue

$$\dbinom{5}{2}\dbinom{15}{2}$$

Exactly two red

$$\dbinom{5}{2}\dbinom{15}{2}$$

Exactly two yellow

$$\dbinom{5}{2}\dbinom{15}{2}$$

Exactly two green

$$\dbinom{5}{2}\dbinom{15}{2}$$

$$4\dbinom{5}{2}\dbinom{15}{2}=4(10)(105)=4200$$

4200 ways

c)

4 balls selected consist of 2 balls each of two different numbers

$$(1, 2, 3, 4), (1,2,3,5), (1,3,4,5), (2,3,4,5)$$

4 ways