Question

Of 19 possible​ books, you plan to take 6 with you on vacation. How many different collections of 6 books can you​ take?

Answer 1

Answer:

27132

Step-by-step explanation:

Assuming the order does not matter, since it will always be a mixture of the same 6 books, we can calculate a combination for these outcomes.

The combination formula is:

nCr = n! ÷ (n-r)!r!

, where ! represents factorials, n represents the total number of items, and r represents the number of items being chosen.

So 19! ÷ (19-6)!6! = 19! ÷ 13! • 6!

19 • 18 • 17 • 16 • 15 • 14 ÷ 6 • 5 • 4 • 3 • 2

= 27132 different combinations of the 6 books.

If you use a calculator, find nCr, plug in 19 for n, and 6 for r.