-1
$\begingroup$

The number of permutation of 3 colors, one of which is red, out of a set of 7 colors, one of which is red, is:

A - 45

B- 90

C- 180

D- 210

Can anyone explain to me why the answer is B please?

Thanks

2 Answers 2

2

One of the colour is red , so red can occupy any one of the 3 available positions. There 6 remaining colors. So other place which red has not occupied cab be occupied in 6 ways. Now there are 5 colors remaining. So the final position can be occupied in 5 ways.

So total number of permutations are 3×6×5=90.

  • 0
    Did you get it? – 2017-02-22
  • 0
    ok, got the first part but why did you only have 5 colors remaining? The total is 7 colors and subtract the red one, are we supposed to have 6 color remaining? – 2017-02-22
  • 0
    For second position red has been used so out of seven 1 is used so 6 remaining. Now for third position there are 5 remaining because out of 7 red is used and another (which can any out of6) is used for second position. – 2017-02-22
  • 0
    For example if second is yellow it then third cannot be red or yellow so there are 5 remaining. – 2017-02-22
  • 0
    Now you got it? – 2017-02-22
  • 0
    got it. thank you so much! – 2017-02-22
0

Select two colours other than red.

$\dbinom{6}{2}$

Arrangements

$3!$

So, required ways is

$\dbinom{6}{2}3!$