𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧: Evaluate (16!-40(14!))/50(13!)

𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:

First, let's simplify the numerator:

16! - 40(14!)

Recall that 16! = 16 × 15 × 14!

So, the numerator becomes:

(16 × 15 × 14!) - 40 × 14!

Factor out 14!:

(16 × 15 - 40) × 14!

Calculate 16 × 15:

16 × 15 = 240

So, the numerator is:

(240 - 40) × 14! = 200 × 14!

Now, let's look at the denominator:

50(13!)

We need to relate 14! to 13!. Recall that 14! = 14 × 13!

Now, divide the numerator by the denominator:

(200 × 14!) / (50 × 13!)

Substitute 14! = 14 × 13!:

(200 × 14 × 13!) / (50 × 13!)

Cancel out 13! from the numerator and the denominator:

(200 × 14) / 50

Simplify the expression:

(200 × 14) / 50 = (4 × 14) / 1

Calculate 4 × 14:

4 × 14 = 56

Therefore, (16! - 40(14!)) / (50(13!)) = 56.