Question

A lock has 5 buttons. The lock is opened by pushing two buttons simultaneously and then by pushing one button alone. How many combinations are possible?

Answer 1

There are 5 choose 2 options for pushing two buttons simultaneously and then 5 options for pushing one button alone

5 choose 2 is 5!/(3!*2!) = 10

10*5 = 50 different combinations

Answer 2

Using the principle of combination, the number of possible combinations for the lock are 50.

Recall :

• nCr = [n! ÷ (n-r)!r!]

2 bottons pusshws simultaneously put of 5 :

5C2 = 5! ÷ (3!2!)

5C2 = (20 ÷ 2) = 10 combinations

1 button pushed alone :

5C1 = 5! ÷ (4!1!)

5C1 = 5 combinations

Total possible combinations = (10 × 5) = 50 combinations

Therefore, there are 50 different possible lock combinations.

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