Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
210
1050
25200
21400
Explanation:
Number of ways of selecting [3 consonants out of 7] and [2 vowels out of 4]
| = (7C3 x 4C2) | |
| =$ \left(\dfrac{7 \times 6 \times 5}{3 \times 2 \times 1} \times\dfrac{4 \times 3}{2 \times 1} \right) $ | |
| = 210. |
Number of groups, each having 3 consonants and 2 vowels = 210.
Each group contains 5 letters.
| Number of ways of arranging 5 letters among themselves= 5!= 5 x 4 x 3 x 2 x 1= 120. |
$\therefore$ Required number of ways = $\left(210 \times 120\right)$ = 25200.