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Binomial Theorem
Mixed Combinatorics A
Mixed Combinatorics B
Mixed Combinatorics C
100
Find the value in the 5th row, entry 1 of Pascal's triangle.
5
100
Three identical door prizes are to be given to three lucky people in a crowd of 100. In how many ways can this be done?
161700
100
How many 4-digit numbers contain no 1's?
8*9*9*9=5832
100
A student must take four final exams, scheduled by a computer, during the morning and afternoon testing periods on Monday through Friday of exam week. If the order of the student's four exams is important, in how many ways can a computer schedule the exams?
10 P 4 = 5040
200
Expand (x + y) ^3 using the binomial theorem.
x ^3 + 3x^2 y ^1 + 3x y^2 + y^3
200
In how many ways can the letters of the word RADISH be arranged?
6!= 720
200
In how many ways can the letters of the word TOMATO be arranged?
6! / 2! = 360
200
There are 3 roads from town A to town B, 5 roads from town B to town C, and 4 roads from town C to town D. How many ways are there to go from A to D via B and C?
3 x 5 x 4 = 60
300
In the expansion of (x - 3 )^15, find the coefficient of the term containing x^13.
945
300
A teacher must pick 3 high school students from a class of 30 to prepare and serve food at the junior high school picnic. How many choices are possible?
24360
300
The locks on the gym lockers have dials with numbers from 0 to 39. Each locker combination consists of 3 numbers. Pythagoras remembers that his numbers are 8, 15, and 17, but he can't remember in which order they appear. If he can try one possibility every 10 seconds, what is the maximum amount of time that is would take him to find the right combination?
3! x 10 second = 60 seconds
300
In how many ways can 8 jackets of different styles by hung in a closet?
8! = 40320
400
In the expansion of (x^2 - 2)^15, find the coefficient of x^12.
-2562560
400
There are 15 people competing in a race. The top 4 get recognition. How many different ways can the top 4 be ordered?
32760
400
Five girls and five boys stand in a line. How many arrangements are possible if all the boys and girls stand alternately?
5!*5!*2 = 28800
400
How many 4 - digit numbers contain at least one 3?
9000 - 8*9*9*9 = 3168
500
The expansion of this binomial (2x + ay)^n gives a term of 5000x^2y^3. Find the values of a and n
What is a=5 n=5
500
In the World Series, two teams, A and B, play each other until one team has won 4 games. For example the "word" ABBAAA represents a 6-game series in which team A wins games 1, 4, 5, and 6. What is the number of possible different 6-game series won by team A?
10 - draw a possibility tree for a 6 game series and only count the ones where A wins
500
A flower shop sells 4 different colored roses. In how many ways can you buy 18 assorted roses?
C (21,18) = 1330
500
In the tennis championship between players A and B at Wimbledon, the first player to win 3 sets is champion. Find the number of different ways for player A to win the championship.
possibility tree counting only the ways in which A wins the match = 15