1. in a college, each student id card is linked with a unique 5-digit pin from the set {0,1,2,3,4,5,6,7,8,9}. a) find the number of id cards possible. b) find the number of id cards possible if the 5-digit number is an odd number? c) recalculate a& b if the digits are not allowed to be repeated

a) The number of ID cards possible is 59049.

b) The number of ID cards possible is 32805.

c) If the digits are not allowed to be repeated, the number of ID cards is 15120.

Step-by-step explanation:

a) We can choose each digit from the set {0,1,2,3,4,5,6,7,8,9} which is made from 9 digits. We need to find a 5-digit pin.

The number of ID cards possible would be: 9 x 9 x 9 x 9 x 9 = = 59049

b) If the 5 digit number is an odd number, then we have to choose between the digits {1,3,5,7,9} for the last digit.

The number of ID cards possible would be: 9 x 9 x 9 x 9 x 5 = 32805

c) If the digits are not allowed to be repeated, then we would have 9 options for the first digit, then 8, then 7...

The number of ID cards possible would be: 9 x 8 x 7 x 6 x 5 = 15120