Question

19. In how many ways the vowels of the word 'ALLAHABAD will occupy the even places
(a) 120
(d) None
(b) 60
(c) 30​

Answer 1

In 60 ways the vowels of the word 'ALLAHABAD will occupy the even places

Solution:

Given that,

In how many ways the vowels of the word 'ALLAHABAD will occupy the even places

A L L A H A B A D

The vowels are a, a, a, a

Therefore, there are 4 vowels

In the word, ALLAHABAD

OEOEOEOEO ( O is odd place and E is even place)

Here total 9 places, 5 odds and 4 even places

Therefore, number of ways to arrange four 'A' at 4 places is given as:

$Number\ of\ ways = \frac{4P4}{4 !}\\\\Number\ of\ ways = \frac{24}{4 \times 3 \times 2 \times 1}\\\\Number\ of\ ways = 1$

Also,

consonants in ALLAHABAD =  L ,L , H, B, D = 5

There are two "L"

The number of ways to arrange 5 consonants where there are 2 'L' is:

$\rightarrow \frac{5 !}{2 !} = \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} = 60$

Total number of ways = 1 x 60 = 60

Thus in 60 ways the vowels of the word 'ALLAHABAD will occupy the even places

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