Question

Seven people are in an elevator which stops at ten floors. In how many ways can they get off the elevator?

10^7

C(10,7)

7^10

P(10,7)

A hiking group consists of 12 students and 2 leaders. A leader must be at the front and back of the line. How many ways can the group hike in a line?

14!

12!*2!

14!/2!

12!

Answer 1

Question 1

Seven people are in elevator, which stops at ten floors.

We have to find in how many ways can these 7 people can get off the elevator.

Now, the first person can get off at 10 floors. So, he or she has 10 options.

Irrespective of this choice, the second person can also get off at any of the ten floors. So, the second person also has 10 options.

Similarly, the third person can also have 10 options of getting off.

Thus, all persons have 10 options, ie. 10 floors for getting off.

So, by multiplication rule of combination,

The number of ways in which 7 people can get off at 10 floors, is

So, the correct option is (A) 10^7.

Question 2

A hiking group consists of 12 students, and 2 leaders.

A leader must be at the front and at the back of the line.

Now, the leaders can be arranged at the front and at the back positions, in 2! ways.

Now, 12 students in the middle can be arranged among themselves, in 12! number of ways.

So, by multiplication rule of combination, all the people can be arranged in

= 12!*2! ways.

So, the correct option is (B) 12!*2!.