Question -
Answer -
Given:
The word ‘MONDAY’
Total letters = 6
(i) 4 letters are used ata time
Number of ways = (No.of ways of choosing 4 letters from MONDAY)
= (6C4)
By using the formula,
nCr = n!/r!(n – r)!
6C4 = 6! / 4!(6 – 4)!
= 6! / (4! 2!)
= [6×5×4!] / (4! 2!)
= [6×5] / (2×1)
= 3×5
= 15
Now we need to findthe no. of words that can be formed by 4 letters.
15 × 4! = 15 ×(4×3×2×1)
= 15 × 24
= 360
∴ The no. of wordsthat can be formed by 4 letters of MONDAY is 360.
(ii) all letters are usedat a time
Total number ofletters in the word ‘MONDAY’ is 6
So, the total no. ofwords that can be formed is 6! = 360
∴ The no. of wordsthat can be formed by 6 letters of MONDAY is 360.
(iii) all letters are usedbut first letter is a vowel ?
In the word ‘MONDAY’the vowels are O and A. We need to choose one vowel from these 2 vowels for thefirst place of the word.
So,
Number of ways = (No.of ways of choosing a vowel from 2 vowels)
= (2C1)
By using the formula,
nCr = n!/r!(n – r)!
2C1 = 2! / 1!(2 – 1)!
= 2! / (1! 1!)
= (2×1)
= 2
Now we need to findthe no. of words that can be formed by remaining 5 letters.
2 × 5! = 2 ×(5×4×3×2×1)
= 2 × 120
= 240
∴ The no. of wordsthat can be formed by all letters of MONDAY in which the first letter is avowel is 240.