Combination
9 C 2 = ?
36
The solution of (x+y)0
1
The mathematical technique that determines the number of possible arrangements in collection of items where the order of selections does matter
Permutation
It is a tool in the fields of general mathematics, probability, and statistics that helps calculate the number of possible outcomes by using branches and nodes
Tree Diagram
It is the set of outcomes from an experiment in probability.
Event
If nC12 = nC9 find n.
21
Expand (x+y)3
x3+3x2y+3xy2+y3
What is 6 P 3?
What is 120?
6!/(6-3)!=120
Aling Nenas Carinderia is offering 3 vegetable menu, 4 meat and 4 types of desserts. How many possible combination are possible from the given options
48
3*4*4=48
The collection or a set of all possible outcomes of a random experiment
Sample Space
In how many ways can a coach choose 3 swimmers from among 5 swimmers? Show your solution.
5!/(5-3)!3!=10
How many terms are there in (x+y)5 when expanded
6
In how many ways can a group of 5 students be seated in a coaster consisting 15 chairs?
360360
15!/(15-5)!= 360360
How many possible outcomes are there if a die is rolled 6 times
46656
66=46656
The product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point
Factorial
Out of 16 players, 11 are to be selected for a cricket team. If the wicket keeper and captain are to be always included in each selection, in how many ways, can this be done?
14C11=2002
Since 2 are always included deduct this from 16 and 11
The 7th row of the Pascal Triangle
1, 7, 21, 35, 35, 21, 7, 1
How many possible arrangement is possible using the letters from the word TEETH?
30
5!/2!2! = 30
A fair die is rolled 4 time, cardinality of the event that the sum of the rolls is 5 or less
5
1111 1211 1121 1112 2111
A stock broker wants to assign 20 new clients equally to 4 of its salespeople. In how many different ways can this be done?
11732745024
20!/5!5!5!5!
A group of students consists of 5 boys and 25 girls. how many the number of ways in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team?
1750
30C3-25C3-5C3=4060-2300-10=1750
25C2*5C1+5C2*25C1=1750
What is the ninth term in (x+y)10
45x2y8
How many possible word arrangement is possible using the word EQUATIONS if the word begins and end with a vowel?
2880
5*4*3*2*1*3*2*1*4
A company places 6 digit symbol code for their products which consist of 4 digit that starts with 5 and 2 letter which the first letter is not a vowel. How many codes are possible?
546000
1*10*10*10*21*26=546000
There are 10 people to be seated in a circular table, How many possible arrangement are there if two people refuse to be seated together?
282240
(10-1)! - (9-1)!*2! =362880-80640=282240