Answer to Question #194170 in Discrete Mathematics for Saoirse lei kjelbe

Question

PERMUTATIONS (21 pts)

1.    There are 6 people to be arranged in a line for a concert. How many arrangements are possible? (3 pts)

 

2.    How many strings of length 5 can be formed using the letters QUALITY if

a.   Repetitions are not allowed? (3 pts)

b.   Repetitions are allowed? (3 pts)

c.    Starts with letter L and repetition is not allowed? (3 pts)

 

3.    A group of 25 people are going to run a race. The top three runners earn gold, silver, and bronze medals. How many arrangements are possible? (3 pts)

 

4.    In how many different ways can the letters of the word "CHANGE" be arranged in such a way that the vowels always come together? (3 pts)

 

5.    Find the number of permutations of the word INFORMATION. (3 pts)

 

Answer 1

1) Number of arrangements in which 6 people can be arranged =6 !=720

2) Word' QUALITY" has 7 different digits-

Number of 5 digit strings is-

a) If Repetition is not allowed $=^7P_5=2520$

b) if Repetition is allowed $= 7^5=16807$

c)  Starts with letter L and repetition is not allowed =$1\times ^6P_4=360$

3)Number of arrangement $=^{25}P3=13800$

4)The word "CHANGE" has 2 vowels and 4 consonants

Number of ways in which two vowels can arranged $= 2\times (4+3+2+1)=20 \text{ ways}$

So Number of ways in which word" change" can be arranged so that does not occur two vowels together$=20\times 4!=16\times 24=384$

5) The given word is "INFORMATION"-

Total word=11

Repeated words= 2 I, 2 O, 2 N

Number of permutation $=\dfrac{11!}{2!2!2!}=\dfrac{11!}{8}=4989600$