Question

The number of words which can be formed out of letters a, b, c, d, e, f taken 3 together, each containing one vowel atleast is

• A. ${}^2{P}_1{.}^4{P}_2$
• B. 96
• C. ${}^6{P}_3$
• D. 120

Answer 1

Answer: (B)

96

At least one vowel $=$total words - no vowel vowels

number of letters we have is 6

number of vowels we have is 2

total words ${=}^6{P}_3$

words without vowel is choosing from 4 words ${=}^4{P}_3$

so words with at least one vowel is ${=}^6{P}_3$ $-$ ${}^4{P}_3$

$=96$