Answer:
120
Explanation:
Objective:
Find how many distinguishable ways are there to order the letters in the word GRADE.
Step by step workout:
step 1
Address the formula, input parameters and values to find how many ways are there to order the letters GRADE.
Formula:
nPr = n!
-----------------
(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in GRADE:
n = 5
Distinct subsets:
Subsets : G = 1; R = 1; A = 1; D = 1; E = 1;
Subsets' count:
n1(G) = 1, n2(R) = 1, n3(A) = 1, n4(D) = 1, n5(E) = 1
step 2
Apply the values extracted from the word GRADE 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 GRADE = 120
Hence,
The letters of the word GRADE can be arranged in 120 distinct ways.
Apart from the word GRADE, 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.