Paper 4 , Section II, E

State and prove the Inclusion-Exclusion principle.

The keypad on a cash dispenser is broken. To withdraw money, a customer is required to key in a 4-digit number. However, the key numbered 0 will only function if either the immediately preceding two keypresses were both 1 , or the very first key pressed was 2. Explaining your reasoning clearly, use the Inclusion-Exclusion Principle to find the number of 4-digit codes which can be entered.

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