How Many Ways are There to Order the Letters of Word COMPUTER?
The 8 letters word COMPUTER can be arranged in 40320 distinct ways. The below detailed information shows how to find how many ways are there to order the letters COMPUTER and how it is being calculated in the real world problems.
Distinguishable Ways to Arrange the Word COMPUTER
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 COMPUTER be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word COMPUTER.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters COMPUTER.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in COMPUTER:
n = 8
Distinct subsets:
Subsets : C = 1; O = 1; M = 1; P = 1; U = 1; T = 1; E = 1; R = 1;
Subsets' count:
n1(C) = 1, n2(O) = 1, n3(M) = 1, n4(P) = 1, n5(U) = 1, n6(T) = 1, n7(E) = 1, n8(R) = 1
step 2 Apply the values extracted from the word COMPUTER in the (nPr) permutations equation
nPr = 8!/(1! 1! 1! 1! 1! 1! 1! 1! )
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8/{(1) (1) (1) (1) (1) (1) (1) (1)}
= 40320/1
= 40320
nPr of word COMPUTER = 40320
Hence,
The letters of the word COMPUTER can be arranged in 40320 distinct ways.
Apart from the word COMPUTER, 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.
