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19 July, 04:28

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!

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  1. 19 July, 04:42
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    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.
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