Question -
Answer -
Given:
The word тАШMONDAYтАЩ
Total letters = 6
(i)┬а4 letters are used ata time
Number of ways = (No.of ways of choosing 4 letters from MONDAY)
= (6C4)
By using the formula,
nCr┬а= n!/r!(n тАУ r)!
6C4┬а= 6! / 4!(6 тАУ 4)!
= 6! / (4! 2!)
= [6├Ч5├Ч4!] / (4! 2!)
= [6├Ч5] / (2├Ч1)
= 3├Ч5
= 15
Now we need to findthe no. of words that can be formed by 4 letters.
15 ├Ч 4! = 15 ├Ч(4├Ч3├Ч2├Ч1)
= 15 ├Ч 24
= 360
тИ┤┬аThe no. of wordsthat can be formed by 4 letters of MONDAY is 360.
(ii)┬аall letters are usedat a time
Total number ofletters in the word тАШMONDAYтАЩ is 6
So, the total no. ofwords that can be formed is 6! = 360
тИ┤┬аThe no. of wordsthat can be formed by 6 letters of MONDAY is 360.
(iii)┬аall letters are usedbut first letter is a vowel ?
In the word тАШMONDAYтАЩthe 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┬а= n!/r!(n тАУ r)!
2C1┬а= 2! / 1!(2 тАУ 1)!
= 2! / (1! 1!)
= (2├Ч1)
= 2
Now we need to findthe no. of words that can be formed by remaining 5 letters.
2 ├Ч 5! = 2 ├Ч(5├Ч4├Ч3├Ч2├Ч1)
= 2 ├Ч 120
= 240
тИ┤┬аThe no. of wordsthat can be formed by all letters of MONDAY in which the first letter is avowel is 240.