Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each…
Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is
24800
25100
25200
25400
Solution
3 consonants can be selected from 7 consonante
$={ }^{7} C_{3} \text { ways }$
2 vowels can be selected from 4 vowels
$={ }^{4} C_{2} \text { ways }$
$\therefore$ Required number of words
$={ }^{7} C_{3} \times{ }^{4} C_{2} \times 5 !$
[selected 5 letters can be arrange in $51,$ so got, a different words]
$=35 \times 6 \times 120=25200$