The number of words that can be made by writing down the letters of the word 'CALCULATE' such that each word starts and ends with a consonant, is

Options

A. `(5xx7!)/(2)`
B. `(3xx7!)/(2)`
C. `2xx7!`
D. none of these

Explanation

Required number of words
= Number of words which begin and end with C
+ Number of words which being and end with L
+ Number of words which being with C and end with C
+ Number of words which begin with C and end with T
+ Number of words which begin with T and end with C
+ Number of words which begin with L and end with T
+ Number of word which begin with T and end with L
`=(7!)/(2!2!)+(7!)/(2!2!)+(7!)/(2!)+(7!)/(2!)+(7!)/(2!2!)+(7!)/(2!2!)+(7!)/(2!2!)`
`=6xx(7!)/(2!2!)+2xx(7!)/(2!)=(5xx7!)/(2!)`.