In how many ways can the letters of the word apple can be rearranged?

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10 Questions 10 Marks 10 Mins

As the vowel, A and E will remain at their respective position

⇒ Total number of arrangements = 3!

But due to the repetition of P, we get

⇒ Total number of arrangements will be = 3!/2! = 6/2 = 3

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A P P L E = 5! / 2==60 PERMUTATIONS:

APPLE, APPEL, APLPE, APLEP, APEPL, APELP, ALPPE, ALPEP, ALEPP, AEPPL, AEPLP, AELPP, PAPLE, PAPEL, PALPE, PALEP, PAEPL, PAELP, PPALE, PPAEL, PPLAE, PPLEA, PPEAL, PPELA, PLAPE, PLAEP, PLPAE, PLPEA, PLEAP, PLEPA, PEAPL, PEALP, PEPAL, PEPLA, PELAP, PELPA, LAPPE, LAPEP, LAEPP, LPAPE, LPAEP, LPPAE, LPPEA, LPEAP, LPEPA, LEAPP, LEPAP, LEPPA, EAPPL, EAPLP, EALPP, EPAPL, EPALP, EPPAL, EPPLA, EPLAP, EPLPA, ELAPP, ELPAP, ELPPA, >Total distinct permutations = 60

The 5 letters word APPLE can be arranged in 60 distinct ways. The below detailed information shows how to find how many ways are there to order the letters APPLE and how it is being calculated in the real world problems.

Distinguishable Ways to Arrange the Word APPLE
The below step by step work generated by the word permutations calculator shows how to find how many different ways can the letters of the word APPLE be arranged.

Objective: Find how many distinguishable ways are there to order the letters in the word APPLE.

Step by step workout:

Input parameters and values:

n1(A) = 1, n2(P) = 2, n3(L) = 1, n4(E) = 1

step 2 Apply the values extracted from the word APPLE in the (nPr) permutations equation

= 1 x 2 x 3 x 4 x 5/{(1) (1 x 2) (1) (1)}

= 120/2

Apart from the word APPLE, you may try different words with various lengths with or without repetition of letters to observe how it affects the nPr word permutation calculation to find how many ways the letters in the given word can be arranged.