MATH SOLVE

3 months ago

Q:
# 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!

Accepted Solution

A:

Answer: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 see6!=6*5*4*3*2*15!=5*4*3*2*1So 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)Does4(3)(2)(1)+2(1)=6(5)(4)(3)(2)(1)24 +2 =72026=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)=26(5)(4)=2?No way! That is saying 120=2 which is not true.