Question

How many ways are there to represent 8 as a sum of 4 natural numbers?

Answer along with description....​

Answer 1

Given :  represent 8 as a sum of 4 natural numbers

To Find : Number of ways

Solution:

Represent 8 as sum of 4 natural numbers  

natural numbers   = { 1 , 2 , 3 , 4 ......................}

if order does not matter :

1 + 1 + 1 + 5  = 8

1 + 1 + 2 + 4 =  8

1 + 1  + 3 + 3  = 8

1 + 2 +  2  + 3 = 8

2 + 2  + 2  + 2  = 8

5 Ways to represent 8 as a sum of 4 natural numbers  

if order does matter

1 + 1 + 1 + 5  = 8    can be  in 4!/3!  = 4 Ways

1 + 1 + 2 + 4 =  8   can be in 4!/2!  = 12 Ways

1 + 1  + 3 + 3  = 8  can be in 4!/2!2!  = 6 ways

1 + 2 +  2  + 3 = 8  can be in 4!/2!  = 12 Ways

2 + 2  + 2  + 2  = 8  can be in 1 ways

4 + 12 + 6 + 12 + 1

= 35 Ways

Learn More:

There are eleven different ways of writing 100 in tha form of mixed ...

https://brainly.in/question/11754985

In how many ways can 20 notes of 500 rupees and 18 notes of 2000 ...

https://brainly.in/question/15186754

In how many different ways can you cricket team finish the trophy ...

https://brainly.in/question/17616177