in how many ways can 5 differently colored marbles be arranged in a row?
February 2nd, 2010 | by admin |in how many ways can 5 differently colored marbles be arranged in a row?
A) 50 , B) 1/5! , C) 5! , D) 250 .
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 5×4 combinations, the third marble can be one of 3 remaining colours.
For each of these 5×4x3 combinations, the fourth marble can be one of 2 remaining colours.
For each of these 5×4x3×2 combinations, the last marble can only be the remaining colour.
Total combinations: 5×4x3×2x1 = 5! = 120
6 Responses to “in how many ways can 5 differently colored marbles be arranged in a row?”
By Ross M on Feb 2, 2010 | Reply
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?
References :
By ellioT on Feb 2, 2010 | Reply
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…..
References :
By mathmom28 on Feb 2, 2010 | Reply
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 5×4 combinations, the third marble can be one of 3 remaining colours.
For each of these 5×4x3 combinations, the fourth marble can be one of 2 remaining colours.
For each of these 5×4x3×2 combinations, the last marble can only be the remaining colour.
Total combinations: 5×4x3×2x1 = 5! = 120
References :
By EzEkIeL on Feb 2, 2010 | Reply
c.5
because you can only simultaneously arrange it and does not affect the other marble
References :
By yljacktt81 on Feb 2, 2010 | Reply
C)5!
References :
By CATMAT on Feb 2, 2010 | Reply
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
References :