Question

A collector has 16 bottles. 5 identical blue bottles, 5 identical green bottles and 6 identical purple bottles.

a. How many different ways can he present by putting the 16 bottles in a line?

b. What if he wants to put 5 of the bottles into a bag. How many different(not ordered) bags are possible?

Answer 1

a) here total 16 bottles

So 16 bottles can arrange in 16! ways in a line

So 16! = 20922789888000 way can arrange 16 bottles in a line

b) If he wants to put 5 of the bottles into a bag.

So group of any 5 in a bag order not matter so we need to use combintion of 5 bottles out of 16 bottles

20922789888000   20922789888000

   = --------------------------------- =   ------------------------ = 4368

120* 39916800 4790016000

So there are 4368 different ways bags are possible with 5 bottles ina bag.\

Hope this will help you.

Thank you.