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?

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

50

Step-by-step explanation:

there are 5 choices for pushing 2 buttons and same for pushing one

5 factorial divided by 2 factorial times 3 factorial is 10 so 10 time 5 is 50