Question

there are 4 sets of balls numbered 1 through 4 placed in a bowl. if 4 balls are randomly chosen without replacement, find the probability that the balls have the same number. express your answer as a fraction

Answer 1

1/455

Explanation:

Given:

4 sets of bballs numbered 1 through 4 are placed in a bowl.

So, totally 16 (4 * 4) balls in a bowl.

To be able to solve this, we must resort to combinations, to find the total number of having same number.

Therefore:

`\begin{gathered} _nC_r=(n!)/(r!\cdot(n-r)!) \\ n=16,r=4 \\ \text{ replacing} \\ _(16)C_4=(16!)/(4!\cdot(16-4)!)=(16!)/(4!\cdot12!)=1820 \end{gathered}`

The probabilitywould be:

`\begin{gathered} p=(4)/(1820) \\ p=(1)/(455) \end{gathered}`

The probability is 1/455