The number of arrangements of the letters of | vedclass

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

Question

(A) The word $BANANA$ contains $6$ letters: $B, A, N, A, N, A$. Here,$A$ appears $3$ times and $N$ appears $2$ times. Total number of arrangements = $

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(A) The word $BANANA$ contains $6$ letters: $B, A, N, A, N, A$. Here,$A$ appears $3$ times and $N$ appears $2$ times. Total number of arrangements = $\frac{6!}{3! 	imes 2!} = \frac{720}{6 	imes 2} = 60$. Number of arrangements where two $N$s are together: Treat $(NN)$ as one unit. Now we have $5$ units: $B, A, A, A, (NN)$. Number of arrangements = $\frac{5!}{3! 	imes 1!} = \frac{120}{6} = 20$. Number of arrangements where two $N$s do not appear adjacently = (Total arrangements) - (Arrangements where $N$s are together) = $60 - 20 = 40$.

The number of arrangements of the letters of the word $BANANA$ in which two $N$s do not appear adjacently is

Similar Questions

$A$ three-digit number $n$ is such that the last two digits are equal and differ from the first digit. The number of such $n$'s is:

How many words comprising of any three letters of the word $UNIVERSAL$ can be formed?

How many $5$-digit numbers can be formed using the digits $3, 4, 7$ once each and the digit $5$ twice?

If the letters of the word $MATHS$ are permuted and all possible words so formed are arranged as in a dictionary with serial numbers,then the serial number of the word $THAMS$ is

If the letters of the word $MOTHER$ are arranged in all possible ways and these words are listed in dictionary order,what is the rank of the word $MOTHER$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module