In how many ways can 5 differently colored marbles be arranged in a row?

Question

in how many ways can 5 differently colored marbles be arranged in a row?

A) 50 , B) 1/5! , C) 5! , D) 250 .

Answer 1

C)5!

Answer 2

C) 5! is the answer

because 5! = 5 * 4 * 3 * 2 * 1

There are 5 spaces for the marbles.

The 1st marble can go in any of the 5 spaces so the number of combinations is 5.

The 2nd marble can only go in 4 of the 5 since 1 space is being occupied by the 1st marble... so the number of combinations is multiplied by 4.

The 3nd marble can only go in 3 of the 5 since 2 spaces are being occupied by the 1st and 2nd marbles... so the number of combinations is multiplied by 3.

so on and so forth.....

Answer 3

The first marble can be one of 5 colours.

For each of these 5 colours, the second marble can then be one of 4 colours.

For each of these 5x4 combinations, the third marble can be one of 3 remaining colours.

For each of these 5x4x3 combinations, the fourth marble can be one of 2 remaining colours.

For each of these 5x4x3x2 combinations, the last marble can only be the remaining colour.

Total combinations: 5x4x3x2x1 = 5!  = 120

Answer 4

It helps if you draw 5 boxes and put the number of choices in each box and then multiply

First box: You have 5 choices, put in number 5

Second box: having already used up 1 marble (in the first box) there are now only 4 options left, put 4 in second box...and so on

5 x 4 x 3 x 2 x 1 = 120 = 5! ways

Answer 5

c.5

because you can only simultaneously arrange it and does not affect the other marble

Answer 6

To put the first marble, you have 5 to choose from.

To put the next one you have 4 to choose from; you have already used one.

And so on.

5 x 4 x 3 x 2 x 1

5!

C

See?