Question:
The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently, is
The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently, is
Updated On: Jun 14, 2022
- 40
- 60
- 80
- 100
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The Correct Option is A
Solution and Explanation
Total number of arrangements of word BANANA
$ \, \, \, \, \, \, \, \, \, \, =\frac{6!}{3!2!}=60$
The number of arrangements of words BANANA in which two N's appear adjacently $=\frac{5!}{3!}=20$
Required number of arrangements $= 60 - 20 = 40$
$ \, \, \, \, \, \, \, \, \, \, =\frac{6!}{3!2!}=60$
The number of arrangements of words BANANA in which two N's appear adjacently $=\frac{5!}{3!}=20$
Required number of arrangements $= 60 - 20 = 40$
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Concepts Used:
Permutations
A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:
\(^nP_r = \frac{n!}{(n-r)!}\)
nPr = permutation
n = total number of objects
r = number of objects selected
Types of Permutation
- Permutation of n different things where repeating is not allowed
- Permutation of n different things where repeating is allowed
- Permutation of similar kinds or duplicate objects