Question

Out of 9 consonants and 3 vowels, how many words of 4 consonants and 2 vowels can be formed?
O 272160.0
720.0
O 378.0
90720.0
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Answer 1

Answer:

272160

Step-by-step explanation:

4 consonant from 9 therefore 9C4

2 vowels from 3 therefore 3C2

Total 6 alphabet therefore they could be arranged 6! times among themselves

therefore

total = 9C4 * 3C2 * 6! = 272160

Answer 2

Answer:

The answer is 272160

step-by-step explanation:

Permutation & combination are 2 ways to express a collection of objects by picking some elements from a set and building subsets. It lists all of the possible arrangements for a specific collection of data. Combinations are the order in in which they are shown, whereas permutations are the choice of information or entities from a set.

The act of placing all the components of a set into a certain order or sequence is known as permutation in arithmetic. In other terms, the procedure of permuting is the reordering of the components of a set if the set is already ordered. Nearly all areas of mathematics involve permutations in some form or another. When different orderings on specific limited sets are taken into consideration, they commonly occur.

$4$ consonant from $9$ therefore $^{9} C_{4}$

$2$ vowels from $3$ therefore $^{3}C_{2}$

There are 6 letters total, therefore they can be put among one another 6! times.

$total=^{9}C_{4} *^{3}C_{2} *6!$

        $= 272160$

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