Permutation and CombinationMedium
Question
The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is:
Options
A.2670
B.2840
C.2920
D.3600
Solution
Sol. [Key Concept: INCONSEQUENTIAL has $5$ distinct vowels and $6$ distinct consonants; choose $2$ of each and arrange: $5C_{2} \times {}^{6}C_{2} \times 4!$.]
INCONSEQUENTIAL contains
(I, E,O, A,U) and (N,C,S,Q,T,L)
Total number of 4 letter words using two vowels and two consonants is
$${= \ ^{5}C_{2} \times \ ^{6}C_{2} \times 4! }{= 3600 }$$
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