With solution please
1.) In how many ways can 6 men be arranged in a row for a show if just 4 men
are capable of acting as end men?
Position the 2 end men
That's 4 end men Position 2 = 4P2 = 4*3 = 12 ways.
For each of those 12 ways to position the end men,
we can Position the 4 remaining men between them:
That's 4 "between"-men Position 4 = 4P4 = 4*3*2*1 = 4! = 24 ways
Answer: 12*24 = 280 ways.
2.) The captain of a basketball team assign himself to the 4th place in the
shooting order. In how many ways can he assign the remaining to his 4
teammates, if just 3 men are considered eligible for the first position?
Position the 1 first place
That's 3 eligible men Position 1 = 3P1 = 3 ways.
For each of those 3 ways to position the first man,
we can Position the 3 remaining men in the 3 other positions
That's 3 men Position 3 = 3P3 = 3*2*1 = 3! = 6 ways
3.) A college freshman must take Mathematics, an English and a Social Science
subjects. If he may select 3 Mathematics subjects, and any of ??? English
subjects and any of 5 Social Science subjects, in how many ways can he arrange
his program?
You forgot to put how many English subjects.
3*???*5
4.) Each license plate in a certain state consists of three letters followed by
two numbers with repetition allowed. How many different license plates are
possible in this state?
Position first letter any of 26 ways.
Choose second letter any of 26 ways.
Choose third letter any of 26 ways.
Choose first digit any of 10 ways.
Choose second digit any of 10 ways.
Answer: 26*26*26*10*10 = 1757600 license plates
Edwin