In: Statistics and Probability
Consider arrangements of the letters NEWBIT. How many arrangements start or end with a vowel?
The individual letter in NEWBIT are:
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 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
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