Question

in how many ways word BINOMIAL can be written, if vowel words are not together?​

Answer 1

Number of ways word BINOMIAL can be written, if vowel words are not together

Step-by-step explanation:

The total number of ways of arranging BINOMIAL= 8!

Number of vowels in the word BINOMIAL= 4  (i, i, o. a)

The total number of ways that vowels can be arranged = 4!

The total number of groups when the vowels are in one group and the rest are individuals= 5!

Number of ways that vowels come together= 5!4!

No vowel together= 8! - 5!4!

                              = 37,440

Answer is 37,440

Answer 2

Word BINOMIAL can be written, if vowel words are not together is 37440 ways.

Step-by-step explanation:

To find : In how many ways word BINOMIAL can be written, if vowel words are not together?​

Solution :

The number of letters in a word BINOMIAL is 8.

The number of ways of arranging is 8!.

The vowels in the alphabet are (a,e,i,o,u).

Number of vowels in the word BINOMIAL (i, i, o, a) = 4

The number of ways that vowels can be arranged is 4!

The total number of groups when the vowels are in one group and the rest are individuals= 5!

Number of ways that vowels come together= $5! \times 4!$

When vowel words are not together = $8! - 5! \times 4!$

$n=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1-(5\times 4\times 3\times 2\times 1)\times(4\times 3\times 2\times 1)$

$n=40320-(120)\times(24)$

$n=40320-2880$

$n=37440$

Therefore, word BINOMIAL can be written, if vowel words are not together is 37440 ways.

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