Combinatorics
Math ⇒ Statistics and Probability
Combinatorics starts at 9 and continues till grade 12.
QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Combinatorics.
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See sample questions for grade 11
A bag contains 5 red, 4 blue, and 3 green balls. In how many ways can 3 balls be drawn from the bag?
A class has 12 students. In how many ways can a group of 5 be selected if two particular students must be included?
A committee of 4 is to be chosen from 7 people. In how many ways can this be done?
A password consists of 2 letters followed by 3 digits. How many different passwords can be formed if repetition is allowed?
A team of 3 is to be formed from 6 boys and 4 girls. How many teams can be formed with at least one girl?
How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated?
How many 4-letter words can be formed from the letters A, B, C, D, E if repetition is not allowed?
How many different ways can 5 books be arranged on a shelf?
How many ways can 3 boys and 2 girls be seated in a row if all boys must sit together?
How many ways can 8 people be seated in a row if two particular people must not sit together?
How many ways can a president, vice-president, and secretary be chosen from a group of 10 people?
If 4 people are to be seated around a round table, how many distinct seating arrangements are possible?
If nC2 = 28, what is the value of n?
If nPr = 60 and nCr = 10, what is the value of r?
If the letters of the word 'PROBABILITY' are arranged, how many different arrangements are possible?
What is the value of 7 choose 3 (written as 7C3)?
A committee of 6 is to be formed from 10 men and 8 women. In how many ways can the committee be formed if it must contain at least 2 women?
A group of 12 students is to be divided into 3 teams of 4 students each. In how many ways can this be done if the teams are unlabeled (i.e., the order of teams does not matter)?
A school club has 8 members. In how many ways can a president, a vice-president, and a secretary be chosen if no person can hold more than one position and two particular members refuse to serve together in any position?
How many different 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, and 7 if each digit is used at most once and the number must be even?
