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?
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Answer 1

Answer:

2880

Step-by-step explanation:

3 vowels to be selected in 4 positions(odd)=4c3

3 vowels can be placed in 3! ways.

Remaining 5 consonants can be placed in 5! ways.

So, 4c3*3!*5!=2880.

Hope it is helpfull!!

Answer 2

Answer:

the word "KEYWORD" is arranged in such a way that the vowels are  to occupy only odd places is $2880$

Step-by-step explanation:

Given:

To arrange the word "KEYWORD" in such a way that the vowels are  to occupy only odd places.

As there are three vowels but there are four odd places so we arrange them in $4C_3$ ways.

The three vowels interchange in $3!$ ways.

The otther five places are interchanging in $5!$ ways.

So the required will be

$4C_3*3!*5!=2880$