Question

sum of three whole numbers a b and c is 10. how many ordered triplets (a b c) exist?

Answer 1

Answer:

30 thirty is the answer of your question

Answer 2

Concept:

To answer this question, let's recall the definition of combination.

Combinations is a concept using which each of the different groups or selections can be made out of a given number of things taking one/some or all at a time.

The formula required: ⁿCₓ= n!/(n-r)! r!

Given:

We are given variables a,b, and c that is taken as whole numbers.

To find:

We are asked to find how many whole numbers exist such that they give a sum of 10.

Solution:

To solve this question we can use our visualisation taking an example.

Now, since we need the sum of 10. So, we place 10 sticks as shown below:

|   |   |   |    |    |    |    |   |    |

Now the question of getting the sum of three whole numbers becomes equivalent to placing two '+' in between the sticks above.

For instance, we have:

|    |    |    |    | + |   | + |   |    |

here, a=5,b=2 and c=3

Hence, from the above illustration, we find that we are given 10 slots out of which we have to choose where to place the two plus signs,

So, from combinations we have

=¹⁰C₂ (using the formula ⁿCₓ)

=10!/(10-2)! 2! (using the formula of combination)

=10!/8! 2!

=10.9.8!/8! 2!

=90/2

=45

Conclusion:

The number of ordered triplets = 45