Please help! Using discrete mathematicals, please use Permutation and combinatio
ID: 3005086 • Letter: P
Question
Please help!
Using discrete mathematicals, please use Permutation and combination for each questions
A large pile of coins consists of pennies, nickels, dimes, and quarters.
A) How many different collections of 30 coins can be cho-
sen if there are at least 30 of each kind of coin?
B)If the pile contains only 15 quarters but at least 30 of each other kind of coin, how many collections of 30
coins can be chosen?
C) If the pile contains only 20 dimes but at least 30 of each
other kind of coin, how many collections of 30 coins can
be chosen?
D) If the pile contains only 15 quarters and only 20 dimes
but at least 30 of each other kind of coin, how many col- lections of 30 coins can be chosen?
Explanation / Answer
Let p, n, d and q be the number of coins respectively
A) Integer solutions to p + n + d + q = 30 is different possible collections.
= (30 + 4 - 1) C (4) = 33C4 = 40,920
B) Total ways - The cases where we pick more than 15 quarters = 33C4 - 17C4
C) Same logic as above: C(33,4) - C(22,4)
D) A - B - C or C(33,4) - C(22,4), C(17,4)