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This is an example of Combination.

Combination is the number of ways of selecting r items from a set of n.

Thus, the formula of Combination is

nCr = n!/r!(n-r)!

There are 8C5 ways that a student can answer 5 out of 8 questions.

Let's solve this.

8C5 = 8!/5!(8-5)!

= 8! / 5!(3!)

= (8×7×6×5!) / (5!×3×2×1)

= (8×7×6) / (3×2×1)

= 336 / 6

8C5 = 56 ways

Therefore, there are 56 ways that a student can answer 5 out of 8 questions.

Combination is the number of ways of selecting r items from a set of n.

Thus, the formula of Combination is

nCr = n!/r!(n-r)!

There are 8C5 ways that a student can answer 5 out of 8 questions.

Let's solve this.

8C5 = 8!/5!(8-5)!

= 8! / 5!(3!)

= (8×7×6×5!) / (5!×3×2×1)

= (8×7×6) / (3×2×1)

= 336 / 6

8C5 = 56 ways

Therefore, there are 56 ways that a student can answer 5 out of 8 questions.

The formula is:

C=

where:

n=total number o objects

r=number of objects you need to answer

Substitute:

C=

C=

Cancel out the 6 and the 3! since they have the same value, and then cancel out 5! on both sides since they are the same, then you are left with:

C=8x7

C=56

Hope this helps =)