Question

James copied a symbol on each of 9 equal-sized strips of paper. He put a dot on 2 of them, a dash on 2 of them, and a pound sign on 5 of them. Then, he put all the strips in a hat and pulled out 3 at random. How many different symbol combinations were possible?

Answer 1

To calculate the number of different symbol combinations, you need to consider the number of ways to choose 3 strips from 9 and the distribution of symbols on those strips. Using the combination formula and the permutation formula, the number of different symbol combinations can be calculated as 1260.

Step-by-step explanation:

To calculate the number of different symbol combinations, we need to consider the number of ways to choose 3 strips from 9 and the distribution of symbols on those strips.

First, let's calculate the number of ways to choose 3 strips from 9. This can be done using the combination formula: C(9,3) = 9! / (3!(9-3)!) = 84.

Next, let's consider the distribution of symbols on those 3 chosen strips. We can have combinations like 2 dots, 1 dash and 0 pound signs; 1 dot, 1 dash and 1 pound sign; and so on. We need to calculate all the possible combinations of distributions.

There are 3 types of symbols, so we can distribute them as (2,0,1), (1,1,1), (0,2,1), and (0,1,2). Using the permutation formula, we can calculate the number of combinations for each distribution: P(2,0,1) = 3! / (2!0!1!) = 3, P(1,1,1) = 3! / (1!1!1!) = 6, P(0,2,1) = 3! / (0!2!1!) = 3, P(0,1,2) = 3! / (0!1!2!) = 3.

Finally, we multiply the number of ways to choose 3 strips from 9 by the number of combinations for each distribution: 84 * (3+6+3+3) = 84 * 15 = 1260.

Answer 2

Use nCr to find that 9 C 3 is 84

You can also use the formula n!/(n-r)!*r! where n is your total amount of objects and r is the number of objects that you choose.

:)