Answer to Question #202869 in Statistics and Probability for Max

Question #202869

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?


1
Expert's answer
2021-06-07T13:15:04-0400

a)

4(54)(150)=4(5)=204\dbinom{5}{4}\dbinom{15}{0}=4(5)=20


20 ways


b)

Exactly two blue


(52)(152)\dbinom{5}{2}\dbinom{15}{2}

Exactly two red


(52)(152)\dbinom{5}{2}\dbinom{15}{2}

Exactly two yellow


(52)(152)\dbinom{5}{2}\dbinom{15}{2}

Exactly two green


(52)(152)\dbinom{5}{2}\dbinom{15}{2}


4(52)(152)=4(10)(105)=42004\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)(1, 2, 3, 4), (1,2,3,5), (1,3,4,5), (2,3,4,5)

4 ways




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