The number of arrangements that can be formed from the letters a, b, c , d, e, f taken 3 at a time without repetition and each arrangement containing at least one vowel, is

Question

The number of arrangements that can be formed from the letters a, b, c , d, e, f taken 3 at a time without repetition and each arrangement containing at least one vowel, is (A) 96 (B) 128 (C) 24 (D) 72

Tardigrade Admin · Accepted Answer

There are 2 vowels and 4 consonants in the letters

a, b, c, d, e, f .

If we select one vowel, then number of arrangements

=^{2} C_{1} \times^{4} C_{2} \times 3! = 2 \times \frac{4 \times 3}{2} \times 3 \times 2 = 72

If we select two vowels, then number of arrangements

=^{2} C_{2} \times^{4} C_{1} \times 3! = 1 \times 4 \times 6 = 24

Hence, total number of arrangements

= 72 + 24 = 96

Q. The number of arrangements that can be formed from the letters $a, b, c, d, e, f$ taken 3 at a time without repetition and each arrangement containing at least one vowel, is

$96$

$128$

$24$

$72$

Q. The number of arrangements that can be formed from the letters a,b,c,d,e,f taken 3 at a time without repetition and each arrangement containing at least one vowel, is

96

128

24

72

There are 2 vowels and 4 consonants in the letters a,b,c,d,e,f. If we select one vowel, then number of arrangements =2C1​×4C2​×3!=2×24×3​×3×2=72 If we select two vowels, then number of arrangements =2C2​×4C1​×3!=1×4×6=24 Hence, total number of arrangements =72+24=96

Q. The number of arrangements that can be formed from the letters $a, b, c, d, e, f$ taken 3 at a time without repetition and each arrangement containing at least one vowel, is

$96$

$128$

$24$

$72$