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

The number of $4$ digit even numbers that can be formed using $0, 1, 2, 3, 4, 5, 6$ without repetition is

$4$ buses run between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by a different bus,then the total number of possible ways is:

The range of the function $f(x) = {}^{7 - x}P_{x - 3}$ is

Find the sample space associated with the experiment of rolling a pair of dice (one is blue and the other red) once. Also,find the number of elements of this sample space.

How many $3$-digit numbers can be formed by using the digits $1$ to $9$ if no digit is repeated?

Vedclass Test Series

Exam Paper Generator

Online Exam Module