Short Answer Type
Long Answer TypeA class has 30 students. In how many ways can three prizes be awarded so that:
(a) no students get more than one prize?
(b) a student may get any number of prizes?
Short Answer TypeHow many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed.
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed.
Long Answer TypeShort Answer Type 
Five of the 10-digits (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) are to be used.
The number must start with 67.
Number of ways of filling box (v) = 1 (∵ Only by 6)
m = 1
Number of ways of filling box (u) = 1 (∵ Only by 7)
n = 1
Number of ways of filling box (z) = 8 (∵ 6 and 7 are not allowed)
p = 8
Number of ways of filling box (y) = 7 (∵ Repetition is not allowed)
q = 7
Number of ways of filling box (x) = 6 (∵ Repetition is not allowed)
r = 6
∴ Total number of 5-digit telephone numbers formed = m x n x p x q x r = 1 x 1 x 8 x 7 x 6 = 336
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