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## Here's the Solution to this Question

Explanation:

There are 6 ways to choose the first person, then 5 to choose the next, etc.

Hence the number of possible choices is: $6\times 5\times4\times3\times 2\times 1=6!=720$

(2) QUALITY

(a) Since no letters of word QUALITY are repeated

There are 7 ways to choose the first alphabet of string, then 6 to choose the next, etc.

So, total number of strings of length 5 = $7\times 6\times 5\times4\times3=2520$

(b) If repetitions are allowed

Then, There are 7 ways to choose the first alphabet of string, and 7 to choose the next, etc.

So, total number of strings of length 5 = $7\times 7\times 7\times7\times 7=16807$

Then the string has one alphabet fixed and remaining 4 can be arranged

So, total number of strings = $6\times 5\times 4\times 3=360$

(3) Total number of arrangements = $^{25}P_3=13800\ \ arrange ments\ \ possible$

(4) CHANGE

Vowels in words are : AE

Then $\boxed{AE}CHNG$ can be arranged as : $2\times 5!=240\ \ ways$

SO, there are 240 ways in which the word CHANGE can be arranged such that vowels are always together.

(5) INFORMATION

Number of letters = 11

Repetitions: 'I'=2 times

'N'= 2 times

'0'= 2 times

Hence, Total number of permutations of word = $\dfrac{11!}{2!\times2!\times 2!}=4989600$