How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?

Asked by Aaryan | 1 year ago |  129

1 Answer

Solution :-

Given:

Total number of vowels = 5

Total number of consonants = 17

Number of ways = (No. of ways of choosing 2 vowels from 5 vowels) × (No. of ways of choosing 3 consonants from 17 consonants)

= (5C2) × (17C3)

By using the formula,

nCr = \( \dfrac{ n!}{r!(n – r)!}\)

= 10 × (17×8×5)

= 10 × 680

= 6800

Now we need to find the no. of words that can be formed by 2 vowels and 3 consonants.

The arrangement is similar to that of arranging n people in n places which are n! Ways to arrange. So, the total no. of words that can be formed is 5!

So, 6800 × 5! = 6800 × (5×4×3×2×1)

= 6800 × 120

= 816000

The no. of words that can be formed containing 2 vowels and 3 consonants are 816000.

Answered by Sakshi | 1 year ago

Related Questions

How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

Class 11 Maths Permutations and Combinations View Answer

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Class 11 Maths Permutations and Combinations View Answer

How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if

(i) 4 letters are used at a time

(ii) all letters are used at a time

(iii) all letters are used but first letter is a vowel ?

Class 11 Maths Permutations and Combinations View Answer

There are 10 persons named P1, P2, P3 …, P10. Out of 10 persons, 5 persons are to be arranged in a line such that is each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.

Class 11 Maths Permutations and Combinations View Answer