Question

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

Answer 1

Answer:

1+3+4, 2+6, 1 +7, 1 + 2 + 5,

Answer 2

Answer:

There are 165 ways to represent the natural number 8 as a sum of 4 natural numbers.

Step-by-step explanation:

Step 1: we can use the stars and bars method, which is a combinatorial technique used to count the number of ways to distribute identical objects into distinct groups.

• We can represent the sum of 4 natural numbers that add up to 8 as a sequence of stars and bars, where the stars represent the number of items in each group and the bars represent the boundaries between the groups.
• For example, the sequence "****||**" represents the sum of 4 natural numbers that add up to 8, where the first group has 4 items, the second group has 0 items, the third group has 2 items, and the fourth group has 2 items.

Step 2: Using this method, the number of ways to represent the natural number 8 as a sum of 4 natural numbers can be calculated as:

Number of ways = (number of stars + number of bars - 1) choose (number of bars)

= (8 + 4 - 1) choose (4 - 1)

= 11 choose 3

= 165

To learn more about natural numbers, visit

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