Question

How many combinations without repetition are possible if n = 6 and r = 3?

20
56
27
18

Answer 1

The correct answer is 20.

Explanation:

The number of combinations without repetition, also known as "n choose r" or the binomial coefficient, can be calculated using the formula:

C(n, r) = n! / (r! * (n-r)!)

where "!" denotes the factorial function.

Let's calculate the number of combinations when n = 6 and r = 3:

C(6, 3) = 6! / (3! * (6-3)!)

= 6! / (3! * 3!)

= (6 * 5 * 4) / (3 * 2 * 1)

= 20

Therefore, when n = 6 and r = 3, there are 20 possible combinations without repetition.

Answer 2

A) 20

Explanation:

`\displaystyle _nC_r=(n!)/(r!(n-r)!)\\\\_6C_3=(6!)/(3!(6-3)!)\\\\_6C_3=(6!)/(3!\cdot3!)\\\\_6C_3=(6*5*4)/(3*2*1)\\\\_6C_3=(120)/(6)\\\\_6C_3=20`