How many words can be formed from the letters of the word ‘SUNDAY’? How many of these begin with D?

Question

Philoid · Accepted Answer

There are 6 letters in the word SUNDAY.

Different words formed using 6 letters of the word SUNDAY is P(6,6)

Formula:

Number of permutations of n distinct objects among r different places, where repetition is not allowed, is

P(n,r) = n!/(n-r)!

Therefore, a permutation of 6 different objects in 6 places is

P(6,6) = = = = 720.

720 words can be formed using letters of the word SUNDAY.

When a word begins with D.

Its position is fixed, i.e. the first position.

Now rest 5 letters are to be arranged in 5 places.

Formula:

Number of permutations of n distinct objects among r different places, where repetition is not allowed, is

P(n,r) = n!/(n-r)!

Therefore, a permutation of 5 different objects in 5 places is

P(5,5) = = = = 120.

Therefore, the total number of words starting with D are 120.