PROBLEM:
Find the number of distinguishable permutations of the letters in the word BASKETBALL.
SOLUTION:
a. To find the number of ways you arrange the letters of the word BASKETBALL, we'll use the formula for distinguishable permutation.
• Since there are 10 letters in total and letters A, B and L have been used twice, our given will be n = 10, p = 2, q = 2 and r = 2.
[tex]\begin{gathered}\begin{gathered}\begin{gathered} \large \boxed{ \begin{array}{l}\tt P=\frac{n!}{p!q!r!} = \frac{10!}{2!2!2!}\\ \tt P= \frac{ 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times4\times 3 \times 2 \times 1}{ 2 \times 1\times 2 \times 1 \times 2 \times 1}\\ \tt P= \frac{3 \: 628 \: 800}{8} \\ \tt P= 453 \: 600\end{array}}\end{gathered} \end{gathered} \end{gathered} [/tex]
ANSWER:
• Thus, there are 453, 600 distinguishable permutations of the letters in the word BASKETBALL.
