Ask Question
15 July, 08:00

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

1. you can choose any number of each type?

2. You can choose at most one of type 1 and any number of the other types?

+3
Answers (1)
  1. 15 July, 08:10
    0
    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.
Know the Answer?
Not Sure About the Answer?
Find an answer to your 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 1. you can choose ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers