Question

A shop has 8 different types of postcards and at least 13 of each type. how many selections of 12 postcards are there if

Answer 1

Answer:

Answered

Step-by-step explanation:

It is a combbinatorics problem. let's think as we need to do 8 partitions  

of these 13 to separate the postcards of different types. So The number of

partitions of n=13 into r=8 terms counting 0's as terms as  C(n+r-1,r-1)​.

(a)

Here n=13 and r=8, put it in the above formula so we get C(13+8-1,8-1)= C(20,7)= 77520 selections.

b).

Here, either (i) we can choose none of type I or (ii) we choose one of type I

Case(i): r=7, n=12 (Here we have only 7 types to choose from​)

Case(ii): r=7, n=11 (Here we have only 11 cards to choose and only 7 types to choose them from)​

Case (i) + Case(ii) = ,C(12+7-1,7-1) + C(11+7-1,7-1) = C(18,6) + (17,6) = 18564+12376 = 30940 selections.