ZittyNakaharaid
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in how many ways can a student answer 5 out 8 question ?

Sagot :

Taskmastersid
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.
Xwolfy01xid
This is a combination problem or simply where order doesn't matter
The formula is:
C=[tex]\frac{n!}{(n-r)!r!}[/tex]
where:
n=total number o objects
r=number of objects you need to answer
Substitute:
C=[tex]\frac{8!}{(8-5)!5!}[/tex]
C=[tex]\frac{8x7x6x5!}{3!5!}[/tex]
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 =)

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