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Q.

The letters of the word “FLOWER” are taken at a time and arranged in all possible ways.

The number of arrangements which begin with ‘F’ and end with ‘R’ is:

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a

20

b

18

c

12

d

14

answer is C.

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Detailed Solution

We are given that 4 letters of the word “FLOWER” are taken at a time.
We need to find the no. of arrangements of the 4-lettered words which begin with F and end with R.
Four letter words must be in the form F_ _ R.
So first and last words are already selected, we have to select the remaining 2 from the remaining 4 letters of the word, L, O, W, E.
The 2nd letter can be selected from 4 letters and the 3rd letter can be selected from 3 letters.
So total no. of arrangements of the 4-letter word that begin with F and end with R is

1 × C 4 1 × C 3 1 × 1

C n r = n! r! (n − r)!, = 4 C 3 13 ⇒ 1 × 4 × 3 × 1 = 12 ways

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