a. Arrangements containing 5 different letters from the word AMPLITUDE are to be made.

Find

i. The number of 5-letter arrangements if there are no restrictions,

ii. The number of 5-letter arrangements which start with the letter A and end with the letter E.

b. Tickets for a concert are given out randomly to a class containing 20 students.

No student is given more than one ticket. There are 15 tickets.

i. Find the number of ways in which this can be done.

There are 12 boys and 8 girls in the class. Find the number of different ways in which

ii. 10 boys and 5 girls get tickets,

iii All the boys get tickets.