Decide whether each of the following statements is true. If false, demonstrate why.

a. 6! = 6.5!

b. 4! + 2! = 6!

C. 6!/3!=2!

a is the only true one if you meant 6 times 5!

Step-by-step explanation:

Before we being

n!=n * (n-1) * (n-2) * ... (3) (2) (1)

Example: 5!=5 (4) (3) (2) (1) and 10!=10 (9) (8) (7) (6) (5) (4) (3) (2) (1)

Yes that operation is multiplication.

a) Does 6!=6*5!

Let's see

6!=6*5*4*3*2*1

5!=5*4*3*2*1

So 6*5!=6 (5*4*3*2*1) = 6*5*4*3*2*1=6!

So true!

b) Does 4!+2!=6!?

4!=4 (3) (2) (1)

2!=2 (1)

6!=6 (5) (4) (3) (2) (1)

Does

4 (3) (2) (1) + 2 (1) = 6 (5) (4) (3) (2) (1)

24 + 2 = 720

26=720 (this is not true)

So 4!+2! is not 6!

c) Does 6!/3!=2!?

6!=6 (5) (4) (3) (2) (1)

3!=3 (2) (1)

If you divide 6! by 3!, then the factors 3 and 2 and 1 cancel and you are left with 6 (5) (4).

So the question becomes is 6 (5) (4) = 2!

2!=2 (1) = 2

6 (5) (4) = 2?

No way! That is saying 120=2 which is not true.