Answer:
The answer is 470 191 764
Step-by-step explanation:
Let's see how we got the figure. First, we need to check our data, or the information supplied.
Data:
- There are unlimited pennies, nickels, and dimes. Therefore, it means that Brian can use any one of those to buy his chocolate.
- Second, there is 1414 coins. These coins come in three different forms mentioned in the first point: pennies, nickels, and dimes.
- Thus, we have 3 types of coins.
- We need to use a number of combinations so that none of the combinations is repeated. A formula for n distinct objects taken at different times will be: nCr = C(n,r) = n!/r!(n-r)!
- n = 1414 coins, r is the types of coins = 3
- Therefore, the formula will be:
nCr = 1414!/ 3! (1414-3)!
= 470 191 764
It therefore means that Brian can combine all the 1414 coins in 470 191 764 ways. This makes sense as reflected by the large number of coins he has.
