(d) 196 (e) C(19, 12) (f) C(8, 5) × C(11, 7)
Please answer d, e, and f.
(3) In the first part of this question, I’m asking you to give a background situation for the combinatorics (“counting”) problems in the rest of the question. In parts (b) through (h), you’ll give a question based on that situation for which the calculation I’ve given you would be the correct answer.
Background siutation for the rest of this problem as I would if I were writing a quiz or an example problem:
Combinations and Permutation
When one has to choose among a set of objects or people, then combination is used to find the number of ways. The order in which they are chosen does not matter here.
On the other hand, if one has to find the number of ways of arranging certain objects, then arrangement is used. Here, the order always matter.
For example, find the number of ways in which 4 benches can be occupied by 4 students. Here, first bench is occupied by 4 students, second one with the remaining 3 students, third one with remaining 2 students and 4th bench with the last student. Thus, is the case of permutation as here the order matters.
Now, suppose there are 5 seats and the number of ways of choosing 4 seats for 4 students can be chosen by using combinations. Here, the order does not matter because it does not matter which student is occupying which seat.
The formula for permutation is
When repetition is allowed : nCr
When repetition is not allowed : Pr n=n! n-r!
Formula for combination is Cr n=n! r!×n-r!
(d) 196
(e) C(19, 12)
(f) C(8, 5) × C(11, 7)
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