How many words beginning with C and ending with Y can be formed by usi

1.	How many words beginning with C and ending with Y can be formed by using the letters of the word ‘COURTESY’?
Answer» To find: number of words starting with C and end with Y There are 8 letters in word COURTESY. Here the position of the letters C and Y are fixed which is 1^st and 8^th . - - - - - - C ? ? ? ? ? Y Rest 6 letters are to be arranged in 6 places which can be done in 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. Therefore, total number of words starting with C and ending with Y is 720.

How many words beginning with C and ending with Y can be formed by using the letters of the word ‘COURTESY’?

Answer»

To find: number of words starting with C and end with Y

There are 8 letters in word COURTESY.

Here the position of the letters C and Y are fixed which is 1^st and 8^th .

- - - - - -

C ? ? ? ? ? Y

Rest 6 letters are to be arranged in 6 places which can be done in 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.

Therefore, total number of words starting with C and ending with Y is 720.