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# Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

## Question:

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

A.Â  25200Â  Â  Â  Â  Â  Â  Â  Â B. 21300

C.Â  24400Â  Â  Â  Â  Â  Â  Â  Â D. 210

3 consonants can be selected from 7 consonants in â€‹$$^7C_3$$â€‹Â ways.

2 vowels can be selected from 4 vowels in â€‹$$^4C_2$$â€‹Â ways.

â€‹$$\therefore$$â€‹Â by multiplication principle,Â

the number of selecting 3 consonants and 2 vowels is

â€‹$$=^7C_3 \times ^4C_2$$â€‹Â

â€‹$$=\frac{7!}{3!4!} \times \frac{4!}{2!2!}$$â€‹

â€‹$$=\frac{7.6.5}{3.2.1} \times \frac{4.3}{2.1}$$â€‹

â€‹$$=35 \times 6$$â€‹

â€‹$$=210$$â€‹

Now, the number of ways of arranging 5 letters among themselvesÂ

â€‹$$=5!$$â€‹

=120Â

â€‹$$\therefore$$â€‹Â the total number of words of 3 consonants and 2 vowels

â€‹$$=210 \times 120$$â€‹

â€‹$$=25200$$â€‹

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