Question

Number of arrangements of the letters R, A,
N, K, O, N, E such that neither the
word RANK nor the word ONE appear, is
A
2376
B
2374
C
2378
D
2372​

Answer 1

Given : Arrangements of the letters R, A,  N, K, O, N, E such that neither the  word RANK nor the word ONE appear

To Find : Number of arrangements

A  2376

B  2374

C  2378

D  2372​

Solution:

R A N K O N  E

7 Letters

N is repeated twice

7 letters can be arranged in 7 ! / 2!  =  2520 Ways

RANK appear -

RANK as 1  letter and O , N , E  -  3 Letters

Total 4 Letters

Total Ways  = 4 !  = 24

ONE as 1 letter and R A N K - 4 letters

Total 5 Letters

Total Ways = 5 ! = 120

RANK and ONE both appears  

2!  = 2 Ways  ( these cases are included in both the cases above)

2520 - 24 - 120  + 2

=2378

2378 arrangements of the letters R, A,  N, K, O, N, E such that neither the

word RANK nor the word ONE appear

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