fangtray wrote:Hello could someone please provide answers and explanations for the following?
In how many ways can the letters of the word "Computer" be arranged?
A. Without any restriction
B. M must always occur at the third place.
C. All vowels are together.
D. All the vowels are never together.
E. Vowels occupy the even positions.
Total number of letters in the word COMPUTER = 8
A. Without any restriction, the letters can be arranged in 8! =
40,320 ways.
B. No. of ways so that M must always occur at the third place (one place is fixed in this case) = 7! =
5,040 ways
C. No. of vowels in the word COMPUTER = 3 (O, U, E)
Consider the 3 vowels as 1 letter. Then there are 5 consonants, so it can be done in 6! = 720
Apart from this the 3 vowels can be arranged in 3! = 6 ways
No. of ways to arrange the letters in a way so that all vowels are together = = 720 * 6 =
4,320 ways
D. No. of ways to arrange the letters in a way so that the vowels are never together = 8! - 6! * 3! = 40,320 - 4,320 =
36,000 ways
E. There are 4 even positions that can be filled by the 3 vowels in 4 * 3 * 2 = 24 ways
Now 5 positions are left, which can be filled in 5! = 120 ways
No. of ways to arrange the letters in a way so that vowels occupy the even positions = 24 * 120 =
2,880 ways
