Unique Ways to Arrange Alphabets of Word BILLION
The 7 letters word BILLION can be arranged in 1260 distinct ways. The below detailed information shows how to find how many ways are there to order the letters BILLION and how it is being arranged in the real world problems.
Possible Arrangements of Alphabets in "BILLION"
The 7 letters word BILLION can be arranged in 1260 unique ways. Below is the list of all possible unique arrangements:
Unique Ways to Arrange the Word BILLION
The below step by step work generated by this permutation calculator shows how to find how many different ways, the letters of the word BILLION can be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word BILLION.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters BILLION.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in BILLION:
n = 7
Distinct subsets:
Subsets : B = 1; I = 2; L = 2; O = 1; N = 1;
Subsets' count:
n1(B) = 1, n2(I) = 2, n3(L) = 2, n4(O) = 1, n5(N) = 1
step 2 Apply the values extracted from the word BILLION in the (nPr) permutations equation
nPr = 7!/(1! 2! 2! 1! 1! )
= 1 x 2 x 3 x 4 x 5 x 6 x 7/{(1) (1 x 2) (1 x 2) (1) (1)}
= 5040/4
= 1260
nPr of word BILLION = 1260
Hence,
The letters of the word BILLION can be arranged in 1260 distinct ways.
Apart from the word BILLION, 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.
