The Student Room Group

S1 - Further Probability - Factorials

I'm fairly certain this is a simple concept... but I am struggling to wrap my head around factorials.

I understand that 8! = 8 x 7 x 6 ... x 1, etc. Simple.

But I'm working on the assignment and can't answer:

1) Write in factorial notations:
i) 8 x 7 x 6 / 5 x 4 x 3
ii) 15 x 16 / 4 x 3 x 2

Could someone please explain step by step how to do one of these questions?

Thanks :smile:
Original post by ladolcevita8
I'm fairly certain this is a simple concept... but I am struggling to wrap my head around factorials.

I understand that 8! = 8 x 7 x 6 ... x 1, etc. Simple.

But I'm working on the assignment and can't answer:

1) Write in factorial notations:
i) 8 x 7 x 6 / 5 x 4 x 3
ii) 15 x 16 / 4 x 3 x 2

Could someone please explain step by step how to do one of these questions?

Thanks :smile:


Lets look at the numerator of the first one.

8×7×68\times 7\times 6

Since factorials go down to 1, we'd have to rewrite this as:

8×7×6×5×4×3×2×15×4×3×2×18\times 7\times 6\times \frac{5\times 4\times 3\times 2\times 1}{5\times 4\times 3\times 2\times 1}

=8×7×6×5×4×3×2×15×4×3×2×1=\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{5\times 4\times 3\times 2\times 1}

=8!/5!

Can you take it from there?
Original post by ghostwalker
Lets look at the numerator of the first one.

8×7×68\times 7\times 6

Since factorials go down to 1, we'd have to rewrite this as:

8×7×6×5×4×3×2×15×4×3×2×18\times 7\times 6\times \frac{5\times 4\times 3\times 2\times 1}{5\times 4\times 3\times 2\times 1}

=8×7×6×5×4×3×2×15×4×3×2×1=\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{5\times 4\times 3\times 2\times 1}

=8!/5!

Can you take it from there?


I managed to get to 8!/5! but am lost with what to do after this to be honest :s-smilie:

Thanks
Original post by ladolcevita8
I managed to get to 8!/5! but am lost with what to do after this to be honest :s-smilie:

Thanks


Now work with your original denominator and convert that to factorials.

NOTE: You are not looking to reduce the whole expression down to one single factorial - it doesn't.
Original post by ghostwalker
Now work with your original denominator and convert that to factorials.

NOTE: You are not looking to reduce the whole expression down to one single factorial - it doesn't.


Got it now, thanks! :smile:

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