Question

show that (12!/5!7!) + (12!/6!6!) = (13!/6!7!)​

Answer 1

Answer:

12!6!6!+12!5!7*6/5!7!6!6!=13*12!/6!7!

5!12!6!(6+7)/5!*6!=13*12!

6+7=13

13=13

hence proved

Answer 2

$\frac{12!}{(5!7!)}$ + $\frac{12!}{(6!6!)}$ = $\frac{13!}{(6!7!)}$

Factorial:

The factorial function is a crucial one in mathematics. It is used to determine the number of possible arrangements or the ordered set of integers. Daniel Bernoulli discovered the well-known interpolating function of the factorial function. Many mathematical concepts, such as probability, sequences and series, use the factorial notion. A factorial is a function that multiplies a number by each number below it until one. The factorial of 3 indicates the multiplication of the numbers 3, 2, 1 (i.e. 3! = 3*2*1) and equals 6.

Lets take the question as A+B=C

A=$\frac{12!}{(5!7!)}$

B=$\frac{12!}{(6!6!)}$

C=$\frac{13!}{(6!7!)}$

Simplifying A,

A=$\frac{12*11*10*9*8*7*6*5*4*3*2*1}{5*4*3*2*1*7*6*5*4*3*2*1}$

A=6*11*2*3*2

A=66*12

A=792

Simplifying B,

B=$\frac{12*11*10*9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1*6*5*4*3*2*1}$

B=2*11*3*2*7

B=22*42

B=924

Simplifying C,

C=$\frac{13*12*11*10*9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1*7*6*5*4*3*2*1}$

C=13*2*11*2*3

C=26*66

C=1716

A+B=C

792+924=1716

1716=1716

LHS=RHS

Hence proved.