Question

In: Statistics and Probability

Consider arrangements of the letters NEWBIT. How many arrangements start or end with a vowel?

Consider arrangements of the letters NEWBIT. How many arrangements start or end with a vowel?

Solutions

Expert Solution

The individual letter in NEWBIT are:

  • N - Consonant
  • E - Vowel
  • W -Consonant
  • B - Consonant
  • I - Vowel
  • T - Consonant

Therefore we have two vowels, 4 consonants.

Now, the number of words possible for NEWBIT, starting or ending with a vowel.

CASE 1

Starting with E

  • The first letter should be E - 1 possibilities
  • 2nd,3rd,4th,5th,6th letter can be anything

The total number of letters starting with E are = 1 * 5 * 4 *3 * 2 * 1 = 120

CASE 2

Starting with I - similar to case 1

The total number of letters starting with I are = 1 * 5 * 4 *3 * 2 * 1 = 120

CASE 3

Ending with I - similar to case 1

The total number of letters ending with I are = 5 *4 *3 *2 * 1 * 1 = 120

CASE 4

Ending with E - similar to case 3

The total number of letters ending with E are = 5 *4 *3 *2 * 1 * 1 = 120

CASE 5

Starting and ending with both E and I = (1* 4 * 3 * 2 * 1 * 1)*2 =48

ANSWER -

Hence the number of words possible for NEWBIT, starting or ending with a vowel = 120 + 120 + 120 +120 -48= 432 words

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!


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