Question

How many seven letter words can be formed using the letters of the word ‘BELFAST’?
$
  {\text{A}}{\text{. 1040}} \\
  {\text{B}}{\text{. 5040}} \\
  {\text{C}}{\text{. 2025}} \\
  {\text{D}}{\text{. 1250}} \\
$

Answer 1

Hint – To find the number of words formed, we calculate the number of letters in the given word. Then we apply the formula for the number of possibilities for a seven letter word using 7 letters.

Complete step by step answer:
Given word, BELFAST
The alphabets are B, E, L, F, A, S, and T.
There are 7 alphabets.
We are supposed to find the number of seven letter words by the given 7 letters.
Therefore the word had 7 spaces, i.e. _ _ _ _ _ _ _
The first space has 7 possibilities, any alphabet from the given can be placed.
The second space has 6 possibilities, any alphabet from the given can be placed except the one already placed in the first place.
And so on until the last space.
Hence the number of seven letter words = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040 words.
Hence Option B is the correct answer.

Note – In order to solve such types of questions the key is to understand exactly how many possibilities each space of the 7 letter word can take.
Number of orders of an even = n! where n is the number of pieces to be placed and the symbol ! denotes factorial.