The number of words that can be formed by using the letters of the word CALCULATE such that each word starts and ends with a consonant, are

Step-by-step solution

Word CALCULATE has 9 letters. Out of which ' C ' repeats 2 times, 'A' repeats 2 times, ' L ' repeats 2 times, 'E', 'U' and ' T ' repeats once. There are 5 consonants and 4 vowels. Two consonants out of 5 can take start and end position of the word in ^5 P ₂ ways. And remaining 7 letters can take remaining 7 positions in 7 ! ways. Also, 'C', 'A' and ' L ' repeats twice each. The required number of words that can be formed = 5 p₂ 7 ! 2 ! 2 ! 2 ! = 5 4 3 ! 7 ! 3 ! 2 2 2 = 5 7 ! 2