Question

How many arrangements of the letters of the word "KEYBOARD" can be made if the vowels are
to occupy only odd places in the word arrangement?

Answer 1

Given : KEYBOARD letters  to be arranged

Vowels are  to occupy only odd places in the word arrangement

To Find : How many arrangements of the letters of the word "KEYBOARD" can be made

Solution:

KEYBOARD - 8 letters

Vowels  E ,  O ,  A    - 3

Consonants  K  Y  B  R  D  - 5

1   , 3   ,  5  & 7  are  4 odd position

3 Vowels in 4 odd positions can be arranged in

⁴P₃  = 24  Ways

Now remaining 5 Letters can be arranged in 5!   Ways

= 120

Total ways  = 120 * 24  =  2880

2880 ways arrangements of the letters of the word "KEYBOARD" can be made if the vowels are  to occupy only odd places  

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