PROBLEM:
How many distinguishable permutations can be made from the number 2, 4, 5, 5 and 4?
SOLUTION:
• To find the number of ways you arrange the numbers in 24554, we'll use the formula for distinguishable permutation.
• Since the numbers 4 and 5 have been used twice, our given will be n = 5, p = 2 and q = 2.
[tex]\begin{gathered}\begin{gathered}\begin{gathered} \huge \boxed{\large \begin{array}{l}\tt P=\frac{n!}{p!q!} = \frac{5!}{2!2!}\\ \tt P= \frac{ 5 \times4\times 3 \times 2 \times 1}{ 2 \times 1 \times 2 \times 1 }\\ \tt P= \frac{120}{4} \\ \tt P= 30\end{array}} \end{gathered} \end{gathered} \end{gathered} [/tex]
ANSWER:
• Thus, there are 30 ways you can arrange the given numbers or what we call the distinguishable permutations.
