Daily Living
You have a basket of 6 different fruits (Apple, Banana, Orange, Mango, Grape, and Pear). You want to select 3 fruits for a smoothie. How many different selections can you make?
20.
Monika is the card dealer in a poker game. In a standard deck of 52 cards, she pulls out four aces then shuffles the remaining cards. What’s the probability of the 5 players getting an Ace?
0, because she already pulled out the Aces which are only 4
A committee of 3 members is to be chosen from
a group of 7 people. In how many ways can this be done?
37
C (n,2)=10. What is n?
5
This formula calculates how many ways one can choose r items from a set of n items, where order doesn't matter.
nCr or C (n, r)
A school club has 10 members, and a 3-person committee needs to be chosen. How many different committees can be formed?
120 different committees.
The Salesman has a 6 chamber revolver and loads in 2 bullets, with 4 being blanks. He and you take turns pulling the trigger. What is the probability that you survive if you go first, if we assume the gun won’t spin after each shot?
4/6 or ⅔
A box contains 10 different colored balls. How many ways can you choose 4 balls from the box?
210
P(n,2)= 42. what's n?
7
It is important to take note of the arrangement of the given items in this calculation.
Permutation
You have 5 different books, and you want to arrange 3 of them in a row. How many ways can you do this?
60 different arrangements
Gihun needs to predict the top 3 horses in a horse race with 8 horses. How many ways can he predict the winning horses?
336
In a class of 12 students, 5 students are to be selected for a group project. How many different selections can be made?
792
C (n,3)=20. what is n?
What does the "!" symbolize?
Factorial of a Number
In a singing contest with 8 participants, how many ways can you assign 1st, 2nd, and 3rd place winners?
336 different ways.
The slot machine at Hakari’s has three slots, displaying 10 different symbols. If each of the slots lands by itself, how many different ways could you get the outcomes?
1,000
How many different 3 digit numbers can be formed using the numbers 1 to 5 without repetition?
60
P(n,3) = 210. what's n?
7
What should be used to calculate the permutation's value of a given problem where r items are taken from n items concerning their order?
nPr or n!/(n-r)!
A security system requires a 4-letter code using the letters A, B, C, D, and E, with no repetition. How many different codes can be made?
120 different codes
The phantom thieves are planning a casino heist, with Joker personally aiming to swap a losing ticket for the winning lottery ticket. The machine will randomly pick 5 numbers from 1 to 50, and all combinations are equally likely. What’s the probability that Joker’s fake ticket matches the winning combination?
1 / 2, 118, 760
A password consists of 4 different letters from the alphabet, how many such passwords can be formed if order matters?
358,800
C (n,4)= 35. what's n?
7
Give the general formula for permutations with repetitions, where n is the total number of items and k represents the number of repetitions of each item.
n!/(1k!)(2k!).....(10K!)