Question

A shop has four types of flowers namely - tulip, rose, marigold and lily. A person came in to buy 10 flowers such that he has at least one flower of each type. In how many ways can he do so, if the shop has sufficient amount of flowers of each type?

Answer 1

atleast one flower of each type.

so 1 tuplip 1 rose 1 marogold 1 lily =4 ways

which is 1 way the rest 6 flowers can be picks as follows 6C4 =6*5*4*3/4*3*2*1 = 15

4*15=60

Answer 2

Given: A shop has four types of flowers namely - tulip, rose, marigold and lily. A person came in to buy 10 flowers such that he has at least one flower of each type.

To find: In how many ways can he do so, if the shop has sufficient amount of flowers of each type.

Solution:

In order to find the number of ways in which a particular event can occur, permutations can be used. The calculation of the permutation can be done by using the following formula.

$P = \frac{n!}{(n-r)!}$

Here, n is the total number of flowers that the person buys, are is the number of types of flowers available and '!' denotes factorial.

$P = \frac{10!}{6!}$

   $= 5040$

Therefore, he can do so in 5040 ways, if the shop has sufficient amount of flowers of each type.