Question

Evaluate this; $\dfrac{{30!}}{{28!}}$
A. 970
B. 870
C. 770
D. 670

Answer 1

Hint: Here we will try to expand both 30! and 28! and then we will cancel the common terms . At last we will multiply the remaining quantities to get to the required answer.

Complete Step-by-Step solution:
We know that $30! = 30 \times 29 \times 28 \times 27 \times 26 \ldots \ldots \ldots \times 1$
And $28! = 28 \times 27 \times 26 \times 25 \ldots \ldots \ldots \times 1$
Therefore,
$\dfrac{{30!}}{{28!}} = \dfrac{{30 \times 29 \times 28 \times 27 \times 26 \ldots \ldots \ldots \times 1}}{{28 \times 27 \times 26 \times 25 \ldots \ldots \ldots \times 1}}$
$ \Rightarrow \dfrac{{30!}}{{28!}} = 30 \times 29 = 870$ ( cancelling common part )

Note: In this particular problem we should recall the method to solve questions related to factorial and its expansion. We can individually solve 30! and 28! and then divide them but it would be a very long process that is the reason to cancel the smaller quantity beforehand.