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

1.	How many words can be formed from the letters of the word ‘SUNDAY’? How many of these begin with D?
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) = \(\frac{6!}{(6-6)!}\) = \(\frac{6!}{0!}\) = \(\frac{720}{1}\) = 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) = \(\frac{5!}{(5-5)!}\) = \(\frac{5!}{0!}\) = \(\frac{120}{1}\) = 120 Therefore, the total number of words starting with D are 120.

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

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) = \(\frac{6!}{(6-6)!}\) = \(\frac{6!}{0!}\) = \(\frac{720}{1}\) = 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) = \(\frac{5!}{(5-5)!}\) = \(\frac{5!}{0!}\) = \(\frac{120}{1}\) = 120

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