From 5 consonants and 5 vowels,how many words | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) We need to form words using $3$ consonants and $2$ vowels from $5$ consonants and $5$ vowels.First,we select the consonants and vowels:Number of w

Vedclass · Accepted Answer

$12000$

Vedclass · Answer

(A) We need to form words using $3$ consonants and $2$ vowels from $5$ consonants and $5$ vowels.First,we select the consonants and vowels:Number of ways to select $3$ consonants from $5$ is ${}^5C_3 = \frac{5 	imes 4}{2 	imes 1} = 10$.Number of ways to select $2$ vowels from $5$ is ${}^5C_2 = \frac{5 	imes 4}{2 	imes 1} = 10$.Total ways to select the letters = $10 	imes 10 = 100$.Now,these $5$ selected letters can be arranged among themselves in $5!$ ways.$5! = 5 	imes 4 	imes 3 	imes 2 	imes 1 = 120$.Total number of words formed = $100 	imes 120 = 12000$.

From $5$ consonants and $5$ vowels,how many words can be formed using $3$ consonants and $2$ vowels?

Similar Questions

The number of ways a committee of $8$ members can be formed from a group of $10$ men and $8$ women such that the committee contains at most $5$ men and at least $5$ women is:

$^{14}C_4 + \sum_{j=1}^{4} {^{18-j}C_3}$ is equal to

$A$ bag contains $5$ red marbles,$4$ black marbles,and $3$ white marbles. The number of ways in which $4$ marbles can be drawn so that at most $2$ of them are red is:

The number of ways of forming the ordered pairs $(p, q)$ such that $p > q$ by choosing $p$ and $q$ from the first $50$ natural numbers is

If $^8C_r = ^8C_{r+2}$,then the value of $^rC_2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module