4. The number of words that can be formed of letters a,
b, c, d taken two or more at a time are
(ay/60
(b) 55
(c) 50
(d) 45
None of these
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Answer:
Answer
a,e - vowels - 2 nos
b,c,d,f - constant - 4 nos
Case 1 : 1 vowel is selected
out of 2 vowels, 1 can be selected in
2
C
1
ways =2
out of 4 constants, 2 constants can be selected in
4
C
2
=
2×1
4×3
=6 ways.
All three letters can arrange among themselves in 3! ways
Thus total possibility = 2×6×3!
=2×6×6=72
Case 2 : 2 vowels is selected
2 vowels can be selected in
2
C
2
ways = 1
1 constant can be arranged in 3! ways
Thus,
total possibility = 1×4×3!
=1×4×6=24
Thus total number of arrangements
= 72+24
=96
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