Question

Basic Combination Formula (n choose k)

A) n!/(n-k)!
B) n!/(k!)
C) n!/k!
D) (n-k)!/k!

Answer 1

The basic combination formula (n choose k) is represented by option A) n!/(n-k)!. This formula is used to calculate the number of ways to choose k items from a set of n items, without considering the order.

Step-by-step explanation:

The basic combination formula, also known as the 'n choose k' formula, is represented by option A) n!/(n-k)!. This formula is used to calculate the number of ways to choose k items from a set of n items, without considering the order.

For example, if you have 10 distinct items and you want to choose 4 of them, you would use the formula as follows: 10!/(10-4)!. This simplifies to 10!/6!, which is equal to (10x9x8x7x6!)/(6!). The 6! terms cancel out, leaving you with 10x9x8x7 = 5,040 combinations.