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
U
(s,u,n,d,a,y)
|
N
(s,n,d,a,y) |
D
(s,d,a,y) |
A
(s,a,y) |
S
(s,y) |
Y |
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 ways
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 × 5 × 4 × 3 × 2 × 1 = 720
720 words can be formed by the letters of the word ‘SUNDAY.’
