Question

Find the number of different arrangements of the letters in the word (CAVALRY) and illustrate linearly.

(a) Ends with a vowel

(b) Has a consonant in the middle

Answer 1

Solution(a)
Ends with a Vowel
Here we can see that 2 A's as vowels and 5 Consonants
So no. of ways can be letters can be arranged as
(6*5*4*3*2*1*1) = 720
So we can make 720 ways to arrange is that letters will ends with a vowel

Solution(b)
Has a consonant in the middle
Here we can see that 5 consonant so 1 consonant can be selected as 5C1
Here are all possible ways
(6C1*5C1*4C1*5C1*3C1*2C1*1C1)/2!
= 6*5*4*5*3*2*1/2 = 1800

So there are 1800 ways so that consonant will be in the middle.