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 '$BANKING$' consists of $7$ letters: $B, A, N, K, I, N, G$.There are $2$ vowels $(A, I)$ and $5$ consonants $(B, N, K, N, G)$.Since the v

Vedclass · Accepted Answer

$720$

Vedclass · Answer

(D) The word '$BANKING$' consists of $7$ letters: $B, A, N, K, I, N, G$.There are $2$ vowels $(A, I)$ and $5$ consonants $(B, N, K, N, G)$.Since the vowels must come together,we treat the group $(AI)$ as a single unit.Now,we have the units: ${B, N, K, N, G, (AI)}$.This gives us $6$ units to arrange,where the letter '$N$' repeats $2$ times.The number of ways to arrange these $6$ units is $\frac{6!}{2!} = \frac{720}{2} = 360$.Within the group $(AI)$,the $2$ vowels can be arranged among themselves in $2! = 2$ ways.Therefore,the total number of arrangements is $360 	imes 2 = 720$.

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

Similar Questions

In how many different ways can the letters of the word '$OFFICES$' be arranged?

If $a$ denotes the number of permutations of $x + 2$ things taken all at a time,$b$ the number of permutations of $x$ things taken $11$ at a time,and $c$ the number of permutations of $x - 11$ things taken all at a time such that $a = 182bc$,then the value of $x$ is

For a set of $5$ true-or-false questions,no student has written all the correct answers,and no $2$ students have given the same sequence of answers. What is the maximum number of students in the class,for this to be possible?

Six objects $O_1$ to $O_6$ are arranged one on top of the other. In how many ways can these be arranged such that $O_1$ and $O_2$ are the $2$ bottom-most objects?

If $^{2n}C_3 : ^nC_2 = 44:3$,then for which of the following values of $r$,the value of $^nC_r$ will be $15$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module