Question

For this problem, your answer can be a numerical expression and does not need to be fully evaluated. For example, you could write 5⋅23+45⋅23+4. A basket contains nine red balls numbered 1, 2, 3, 4, 5, 6, 7, 8, and 9 and nine blue balls numbered 1, 2, 3, 4, 5, 6, 7, 8, and 9.

a) A sample of nine balls are drawn from the basket without replacement. How many distinct samples are possible (assuming that order does not matter)?

b) How many of the samples in a) contain only blue balls?

c) How many of the samples in a) contain seven blue balls?

Answer 1

a)

A sample of nine balls are drawn from the basket without replacement.

The number distinct samples possible are, $({_{}^{18}\textrm{C}_9})$

i.e., The number distinct samples possible are,

18! 99!

b)

The number of samples in a) containing only blue balls is, $({_{}^{9}\textrm{C}_9})$

i.e., The number of samples in a) containing only blue balls is. 1.

c)

The number of samples in a) containing 7 blue balls are, $({_{}^{9}\textrm{C}_7})({_{}^{9}\textrm{C}_2})$

i.e., The number of samples in a) containing 7 blue balls are, $(\frac{9!}{7!2!})(\frac{9!}{2!7!})$

i.e., The number of samples in a) containing 7 blue balls are, $(\frac{8\times 9}{1\times 2})(\frac{8\times 9}{1\times 2})$

i.e., The number of samples in a) containing 7 blue balls are,

i.e., The number of samples in a) containing 7 blue balls are, 1296.