Final answer:
There are 53,769,225 ways to select 9 coins and 56,834,632,664 ways to select 16 coins from $1 worth of identical pennies, nickels, and dimes.
Step-by-step explanation:
To determine the number of ways to pick a selection of coins, we can use the concept of combinations. Since there are 100 pennies, 100 nickels, and 100 dimes, the total number of coins is 100 + 100 + 100 = 300. (a) If you select a total of 9 coins, you can choose different combinations of coins. To find the number of combinations, we use the formula C(n, r) = n! / (r!(n-r)!), where n is the total number of coins and r is the number of coins in the selection. In this case, n = 300 and r = 9. Substituting these values, we find C(300, 9) = 53,769,225 ways to select 9 coins. (b) If you select a total of 16 coins, you can similarly use the combination formula. Substituting n = 300 and r = 16, we find C(300, 16) = 56,834,632,664 ways to select 16 coins.