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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.  25200               B. 21300

C.  24400               D. 210

3 consonants can be selected from 7 consonants in ​$$^7C_3$$​ ways.

2 vowels can be selected from 4 vowels in ​$$^4C_2$$​ ways.

$$\therefore$$​ by multiplication principle,

the number of selecting 3 consonants and 2 vowels is

$$=^7C_3 \times ^4C_2$$​

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

$$=\frac{7.6.5}{3.2.1} \times \frac{4.3}{2.1}$$

$$=35 \times 6$$

$$=210$$

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

$$=5!$$

=120

$$\therefore$$​ the total number of words of 3 consonants and 2 vowels

$$=210 \times 120$$

$$=25200$$

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