Question-21 What is the probability of forming the word from the letters of the word IMPEACH such that all vowels come together?
A) 8/35
B) 1/7
C) 3/35
D) 17/35
Answer: B) 1/7
Explanation
There are 7 letters in the word IMPEACH. There are 3 vowels in the letter = I, E, A
Let the vowel be represented as V
The condition such that all vowels corne together are:
| V | V | V | – | – | – | – |
| – | V | V | V | – | – | – |
| – | – | V | V | V | – | – |
| – | – | – | V | V | V | – |
| – | – | – | – | V | V | V |
Hence, 3 vowels together can be arranged as = 5! x 3!
Then the probability will be:
=\frac{(51 \times 3 !)}{7 !} =\frac{(51 \times 3 !)}{(7 \times 6 \times 5 !)} =\frac{1}{7}