Math Problems

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In order to find the principal and the rate, a system of two equations should be solved. One equation describes the return of the household before the change in principal and interest rate, the other – after the change, as shown below:


In order to find the number of 6-number combinations out of 49 numbers, I need to consider that each number can be drawn only once and that the order in which they are drawn doesn’t matter.
Then, I can conclude that when I am picking 6 numbers, my first choice can include any of 49 numbers available, second choice – any of 48 numbers available (one number is already drawn, so it is not available any more), third choice – any of 47 numbers available, fourth choice – any of 46 numbers available, fifth choice – any of 45 numbers available, sixth choice – any of 44 numbers available.
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