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

ANSWER:

1/455

STEP-BY-STEP 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:

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

The probabilitywould be:

$\begin{gathered} p=\frac{4}{1820} \\ p=\frac{1}{455} \end{gathered}$

The probability is 1/455