Combinatorics
Math ⇒ Statistics and Probability
Combinatorics starts at 9 and continues till grade 12.
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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 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 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?
Which of the following is a correct statement about permutations?
(1) Order does not matter
(2) Order matters
(3) Repetition is not allowed
(4) None of the above
Which of the following is NOT a property of combinations?
(1) nCr = nC(n-r)
(2) nCr = nPr / r!
(3) nCr = n! / (n - r)!
(4) nC0 = 1
Which of the following is the correct formula for the number of combinations with repetition?
(1) n^r
(2) (n + r - 1)! / [r!(n - 1)!]
(3) n! / (n - r)!
(4) r! / (n - r)!
Which of the following is the correct formula for the number of permutations of n objects taken r at a time?
(1) n! / (n - r)!
(2) n! / r!
(3) n^r
(4) r! / (n - r)!
Fill in the blank: The number of ways to arrange n distinct objects in a line is _______.
Fill in the blank: The number of ways to arrange the letters of the word 'LEVEL' is _______.
Fill in the blank: The number of ways to distribute 5 identical balls into 3 distinct boxes is _______.
Fill in the blank: The number of ways to select all or none from n distinct objects is _______.
True or False: The number of combinations of n objects taken r at a time is always less than or equal to the number of permutations of n objects taken r at a time.
True or False: The number of ways to arrange n objects in a circle is (n-1)!
True or False: The number of ways to arrange n objects in a row is always greater than the number of ways to arrange them in a circle for n > 2.
True or False: The number of ways to arrange n objects with some identical objects is n! divided by the product of factorials of identical objects.
