Discrete Mathematics Questions:A die is tossed twice and the numbers showing on the top faces are recorded in sequence.Determine the element in each...

Discrete Mathematics Questions:

1.      A die is tossed twice and the numbers showing on the top faces are recorded in sequence. Determine the element in each of the given events:

a.       At least one of the numbers is 5.

b.       At least one of the numbers is an 8

2.      Solve the recurrence relation: an = 4an-1 + 5an-2 were a1 = 2 and a2 = 6

3.      Calculate: 5!/7!

4.      Calculate 5C5

5.      In how many ways can a five card hand be dealt from 52 cards?