in how many ways can the letters of the word ALGEBRA be arranged without changing the relative order of the - Maths - Permutations and Combinations

Question

in how many ways can the letters of the word ALGEBRA be arranged
without changing the relative order of the vowels and
consonants?

Himanshu · Accepted Answer

In the word ALGEBRA, there are three vowels (A, A and E) and
four consonants (L, G, B and R)
We need to find different arrangements of the word ALGEBRA such
that relative positions of vowels and consonants do not change
Therefore, in the three positions occupied by vowels, we can
rearrange the vowels in 3!/2! = 3 ways
Four consonants can be rearranged in four spaces occupied by
consonants in 4! ways = 24 ways
Therefore, required number of arrangements = 3 x 24 = 72

in how many ways can the letters of the word ALGEBRA be arranged without changing the relative order of the vowels and consonants?