# In how many ways can a student answer 5 out 8 question ?

2
by ZittyNakahara

2015-12-12T08:36:16+08:00

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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.
2015-12-12T16:59:21+08:00
This is a combination problem or simply where order doesn't matter
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 =)