Binomial Expansion
In how many different ways can 9 floats line up for a parade?
9!
9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
362,880
In how many different ways can you answer a 14 question true or false quiz?
2^14
2x2x2x2x2x2x2x2x2x2x2x2x2x2
16,384
Write as a single factorial.
1*2*3*4*....*53
53!
Expand (2x+5)5
32x5+400x4+200x3+5000x2+6250x+3125
The game euchre uses only 24 cards. How many 5-card hands can be made in the game?
24C5
=42,504
Drivers license numbers are made up of 1 letter followed by 8 digits that can be repeated. The first digit cannot be 0. How many different license numbers are possible?
2,340,000,000
26*9*10*10*10*10*10*10*10
Write as a single factorial.
(n-3)(n-4)(n-5)...(1)
(n-3)!
Expand (x-5)3
x3 - 15x2 +75x -125
Your school yearbook has an editor-in-chief and an assistant editor-in-chief. If the yearbook staff has 15 members, in how many different ways can these positions be filled?
15P2
15 x 14
In a certain province, the license plate is made up of 3 letters followed by 4 numbers. If the letters may not be used more than once, and the first number must be greater than 5, but any number can be reused, how many different license plates are possible?
26 x 25 x 24 x 4 x 10 x 10 x 10
62,400,000
Write as a single factorial.
(n+1)(n)(n-1)(n-2)....(1)
(n+1)!
What is the coefficient for the term x7 y2 in the expansion of (x + y)9 ?
36
A customer can choose one of 4 different salad mixes, 3 of 8 different toppings, and one of 5 dressings. How many different salads can s/he create?
4C1x 8C3 x 5C1
160 different salads
Ms. Ani is playing darts and hits the target 15% of the time. If she throws 6 darts, what is the probability that she will hit the target exactly 4 times?
(.15)(.15)(.15)(.15)(.85)(.85)=0.0003658
Write without factorials.
(54!)/(52!)
54*53=2,862
The kickball tournament has each advisory class complete against their own grade level. There are 20 9th grade, 22 10th grade, 18 11th grade and 15 12th grade advisory classes. If the top 2 advisory classes from each grade advance to the finals, how many ways could the 8 finalists be selected?
20C2 * 22C2 * 18C2 * 15C2
= 190 * 231 * 153 * 105 = 705,092,850
Ms. Ani is playing darts and hits the target 15% of the time. If she throws 6 darts, what is the probability that she will hit the target at least 4 times?
About 0.00044174
Add probabilities for 4 or 5 or 6 times.
4 times: 0.0003658
5 times: 0.00006455
6 times: 0.00001139
Write without factorials.
((n+3)!)/((n-1)!)
(n+3)(n+2)(n+1)(n)