How many words can be formed by the letters of the word ‘SUNDAY’?

Solution:

Given: We have 6 letters

To Find: Number of words formed with Letter of the word 'SUNDAY:'

'SUNDAY' consist of 6 letters.

NOTE: - Unless specified, assume that repetition is not allowed.

Let us represent the arrangement with an example

6 ways 5 ways 4 ways 3 ways 2 ways 1 way

We have 6 places

First place can be filled with 6 letters, i.e. S,U,N,D,A,Y = 6 way

Second place can be filled with 5 letters (as one letter is already used in the first place) = 5 ways

Similarly,

Third place can be filled with 4 letters $=4$ ways

The fourth place can be filled with 3 letters $=3$ ways

The fifth place can be filled with 2 letters $=2$ ways

The sixth place can be filled with 1 letters = 1 ways

Total number of letters $=6 \times 5 \times 4 \times 3 \times 2 \times 1=720$

720 words can be formed by the letters of the word 'SUNDAY.'