How Many Ways are There to Order the Letters of Word PHONE?
The 5 letters word PHONE can be arranged in 120 distinct ways. The below detailed information shows how to find how many ways are there to order the letters PHONE and how it is being calculated in the real world problems.
Distinguishable Ways to Arrange the Word PHONE
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 PHONE be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word PHONE.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters PHONE.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in PHONE:
n = 5
Distinct subsets:
Subsets : P = 1; H = 1; O = 1; N = 1; E = 1;
Subsets' count:
n1(P) = 1, n2(H) = 1, n3(O) = 1, n4(N) = 1, n5(E) = 1
step 2 Apply the values extracted from the word PHONE in the (nPr) permutations equation
nPr = 5!/(1! 1! 1! 1! 1! )
= 1 x 2 x 3 x 4 x 5/{(1) (1) (1) (1) (1)}
= 120/1
= 120
nPr of word PHONE = 120
Hence,
The letters of the word PHONE can be arranged in 120 distinct ways.
Apart from the word PHONE, 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.
