Mathematics I - Old Questions
6. In how many ways can be letter of words “Sunday” be arranged? How many of these arrangement begin with S? How many begin with S and don’t end with y?
Answer
AI is thinking...
The word SUNDAY be arranged in 6!=6*5*4*3*2=720 ways
When a word begins with S. Its position is fixed, i.e. the first position. Now rest 5 letters are to be arranged in 5 places. So,
No. of arrangement begin with S = 5! = 120
The are 5! ways of ordering the word SUNDAY if the first letter is restricted to S, because only the 5 remaining ones are allowed to change.
There are 4! ways of ordering the word SUNDAY if the first letter is restricted to S "and" the last letter is restricted to Y
Therefore, there are 5!-4! ways that the word SUNDAY can be arranged such that the first letter is S and the last letter "is not" Y
5!-4! = 120-24 =96