In how many different ways can the letters of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The word '$CORPORATION$' consists of $11$ letters: $C, O, R, P, O, R, A, T, I, O, N$.The vowels are $O, O, A, I, O$ (total $5$ vowels,where $O$ re

Vedclass · Accepted Answer

$50400$

Vedclass · Answer

(D) The word '$CORPORATION$' consists of $11$ letters: $C, O, R, P, O, R, A, T, I, O, N$.The vowels are $O, O, A, I, O$ (total $5$ vowels,where $O$ repeats $3$ times).The consonants are $C, R, P, R, T, N$ (total $6$ consonants,where $R$ repeats $2$ times).Treating the $5$ vowels as a single unit,we have $6$ consonants + $1$ unit of vowels = $7$ items to arrange.The number of ways to arrange these $7$ items,where $R$ repeats $2$ times,is $\frac{7!}{2!} = \frac{5040}{2} = 2520$.Within the vowel unit,the $5$ vowels $(O, O, O, A, I)$ can be arranged in $\frac{5!}{3!} = \frac{120}{6} = 20$ ways.Total number of arrangements = $2520 	imes 20 = 50400$.

In how many different ways can the letters of the word '$CORPORATION$' be arranged so that the vowels always come together?

Similar Questions

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1} - T_n = 10$,then the value of $n$ is:

The number of $6$-digit numbers that can be formed using the digits $0, 1, 2, 5, 7,$ and $9$ which are divisible by $11$ and no digit is repeated,is

Out of $6$ boys and $4$ girls,a group of $7$ is to be formed. In how many ways can this be done if the group is to have a majority of boys?

If the best and the worst paper never appear together,then six examination papers can be arranged in how many ways?

Let $T_n$ denote the number of triangles which can be formed using the vertices of a regular polygon of $n$ sides. If $T_{n + 1} - T_n = 21$,then $n$ equals:

Vedclass Test Series

Exam Paper Generator

Online Exam Module