1. The door of a computing room is fitted with a security pad which has 16 butto

Question

1. The door of a computing room is fitted with a security pad which has 16 buttons, each marked with a different alphanumeric character. A code has to be entered on the pad before the door can be opened. The code consists of 4 different characters chosen from the 16 available. Enter numbers as whole numbers (do not use scientific notation). (a) Assume that the correct 4 characters must be entered in the (one) correct order to open the door. How many different possible codes are there? (2 marks) Number of possible codes- (b) Assume that the correct 4 characters may be entered in any order to open the door. How many different possible codes are there? (2 marks) Number of possible codes

Explanation / Answer

Answer to the question)

Given:

N = 16

X = 4

.

Part a)

Order matters so we apply permutation

16P4 = 16! /(16-4)!

16P4 = 16 *15*14*13*12! / 12!

16P4 = 16 *15 *14 *13

16P4 = 43680

.

Part b)

If order doesnot matter we apply combination

16C4 = 16! / 4!*(16-4)!

16C4 = 16 *15 *14 *13 *12! / 4!*12!

16C4 = 16 *15 *14 *13 /(4*3*2*1)

16C4 = 1820

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