Question

The door on the computer center has a lock which has five buttons numbered from 1 to 5. The combination of numbers that opens the lock is a sequence of five numbers and is reset every week.
(a) How many combinations are possible if every button must be used once?
(b) Assume that the lock can also have combinations that require you to push two buttons simultaneously and then the other three one at a time. How many more combinations does this permit?

Answer 1

Answer:

a) 121 combinations

b) 124 combinations

Step-by-step explanation:

a) 5 possible number without repeating any will give us =

5 possible numbers* 4 possible numbers* 3 possible numbers* 2possible numbers + 1 possible numbers = 121 combination

b) 5 possible number but repeating 1 will give us 5 possible numbers* 4 possible numbers * 3 possible numbers* 2possible numbers

+4 possible number

124 combination

Answer 2

A) Number of possible combinations if every button must be used once is; 120 combinations

B) The number of combinations that the described scenario can permit is; 60 combinations.

A) We are told that the lock has five buttons numbered from 1 to 5. Thus;

Number of possible combinations if every button must be used once = 5!

>>> 5 × 4 × 3 × 2 × 1 = 120 combinationa

B) Since the lock can also have combinations that require pushing two buttons simultaneously and the other 3 one at a time.

This means we will use the combination formula and factorial to get;

5C2 × (3!) = 60 ways

Read more at; https://brainly.com/question/501103