You had to dry the dishes. Too bad. Now as you start on your walk you notice your nephew Jeffrey over in the corner of the room. He has a box of 10 US
quarters, each representing a different state. You stop to watch.
a. He reaches into the box, grabs 4 quarters, and drops them in his pocket.
i. How many different collections of state quarters might he
have dropped in his pocket?
ii. How many different collections of state quarters might he
have left in the box?
iii. Explain the relationship between the answers in i and ii?
b. He replaces the quarters from his pocket into the box. Now he selects 6 quarters from the [refilled] box and lines them up on the table. How
many different arrangements of 6 quarters might he make?
c. Next, he dumps all 10 of the state quarters on the table and lines them up. He puts the Alabama quarter first in the line, the Ohio quarter
second in line, and the Virginia quarter last in the line and arranges the other state quarters in the line randomly. How many different
arrangements of state quarters might he make?
d. Ignoring what states the quarters represent, he flips each of the 10 coins and places them in a line either heads up or tails up, in the order in which he flips them. How many different arrangements of heads and tails in the line might he get?
e. His older sister yells, “I’m tired of you playing with those stupid quarters. If the first three coins you flip are not alike (that is not all heads or all tails) I’m taking all of your quarters.” What is the probability that the first three coins are not alike?