Question:

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

Updated On: Jul 6, 2022
  • $24800$
  • $25100$
  • $25200$
  • $25400$
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The Correct Option is C

Solution and Explanation

Reqd. number of ways $=\,^{7}C_{3}\times\,^{4}C_{2}\times 5!\,\, \frac{7\times6\times5}{1\times2\times3}\times\frac{4\times3}{1\times2}\times120$ $=35\times6\times 120$ $=210\times120$
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Notes on permutations and combinations

Concepts Used:

Permutations and Combinations

Permutation:

Permutation is the method or the act of arranging members of a set into an order or a sequence. 

  • In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point. 
  • A permutation is used in many events of daily life. It is used for a list of data where the data order matters.

Combination:

Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.

  • Combination refers to the combination of about n things taken k at a time without any repetition.
  • The combination is used for a group of data where the order of data does not matter.