Please help. I didn't get the right answer with this before.
A mathematics journal has accepted 14 articles for publication. However, due to budget restraints, only 7 articles can be published this month. How many specific ways can the journal editor assemble 7 of the 14 articles for publication?
Possible answers:
14
3,432
98
17,297,280
14C7=14!/(7!7!)
! means factorial
7!=7×6×5×4×3×2×1
If order is not important
14C7=14!/(7!7!)
! means factorial
7!=7×6×5×4×3×2×1
If order is important, which is not explicit in the question, then the answer is
14P7=14!/7!
To solve this problem, we can use the concept of combinations. A combination is a selection of items without considering their order. In this case, we need to find out how many different combinations of seven articles can be chosen from a set of 14 articles.
The formula to calculate combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of items and r is the number of items we want to choose.
In this problem, we have n = 14 (total number of articles) and r = 7 (number of articles to be chosen).
Plugging these values into the formula, we get:
C(14, 7) = 14! / (7!(14-7)!)
Simplifying further:
C(14, 7) = 14! / (7! * 7!)
Now, let's calculate the factorial values:
14! = 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7!
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
Substituting these values back into the formula, we get:
C(14, 7) = (14 x 13 x 12 x 11 x 10 x 9 x 8 x 7!) / (7! * 7!)
Now, we can cancel out the common terms in the numerator and denominator:
C(14, 7) = (14 x 13 x 12 x 11 x 10 x 9 x 8) / 7!
Calculating further:
C(14, 7) = 17,297,280 / 7!
The value of 7! (7 factorial) is 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040
So, substituting this value back into the formula, we get:
C(14, 7) = 17,297,280 / 5,040
Calculating this division, we find:
C(14, 7) ≈ 3,432
Therefore, there are approximately 3,432 specific ways the journal editor can assemble 7 articles for publication.