Question

Find the number of permutations of the letters in the word: PHILADELPHIA

Answer 1

There are 12 letters in P H I L A D E L P H  I A AND THERE AE:
2 P, 2 H, 2 A, 2 I

Permutation of ¹²P₁₂ = 12! , but mind you there are repeated letters so 
the final Permutation: 12!/(2!)(2!)(2!)(2!) = 29 937 600 ways of arranging letters

Answer 2

The number of permutations in the word PHILADELPHIA is 14968800

The permutation of a variable is the number of possible ways in which a variable can be classified or arranged. It is usually expressed as:

From the word PHILADELPHIA, we have:

• 2P, 2H, 2I, 2L, 2A

• the total number of words (n) in PHILADELPHIA = 12

Using permutation:

$\mathbf{_nP_r = \dfrac{n!}{P! \ H! \ I! \ L! \ A!}}$

$\mathbf{_nP_r = \dfrac{12!}{2! \ 2! \ 2! \ 2! \ 2!}}$

$\mathbf{_nP_r =14968800}$

Learn more about permutation here:

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