How Many Ways are There to Order the Letters of Word JOY?
The 3 letters word JOY can be arranged in 6 distinct ways. The below detailed information shows how to find how many ways are there to order the letters JOY and how it is being calculated in the real world problems.
Distinguishable Ways to Arrange the Word JOY
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 JOY be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word JOY.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters JOY.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in JOY:
n = 3
Distinct subsets:
Subsets : J = 1; O = 1; Y = 1;
Subsets' count:
n1(J) = 1, n2(O) = 1, n3(Y) = 1
step 2 Apply the values extracted from the word JOY in the (nPr) permutations equation
nPr = 3!/(1! 1! 1! )
= 1 x 2 x 3/{(1) (1) (1)}
= 6/1
= 6
nPr of word JOY = 6
Hence,
The letters of the word JOY can be arranged in 6 distinct ways.
Apart from the word JOY, 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.
