Permutations and Combinations quiz

The number of ways of arranging 6 different books on a shelf is:

The value of 7!/5! is:

The number of lines through 10 points, no three of which are collinear, is:

The number of ways of answering 5 true-or-false questions is:

If n!/(n - 2)! = 12, then n is:

8C3 + 8C2 is equal to:

The number of handshakes among 12 people, each shaking hands once with every other, is:

The value of 0! is:

The number of signals made with 2 of 5 different flags placed one below the other is:

The number of 4-digit numbers from the digits 1 to 9 without repetition is:

Evaluate 5P3 and 10C3. (2 marks)

How many 4-letter words, with or without meaning, can be formed from the letters of ROSE without repetition? (2 marks)

Find the number of arrangements of the letters of EXAMINATION. (2 marks)

Prove that nCr = nC(n - r). (2 marks)

How many 3-digit numbers with distinct digits can be formed from 1, 2, 3, 4 and 5? (2 marks)

In how many ways can 4 cards be drawn from a pack of 52 cards so that all are of the same suit? (2 marks)

In how many ways can one card of each suit be drawn from a pack of 52 cards? (2 marks)

How many chords can be drawn through 21 points on a circle? (2 marks)

A committee of 5 is chosen from 4 girls and 7 boys. In how many ways can it have at least 3 girls? (2 marks)

In how many ways can 5 boys and 3 girls stand in a row so that the girls are together? (2 marks)

Find the number of ways of choosing 4 red cards from a pack of 52 cards. (3 marks)

In how many ways can the letters of ASSASSINATION be arranged so that all the S are together? (3 marks)

Find n if (n + 1)! = 12 x (n - 1)!. (3 marks)

How many 4-digit numbers greater than 5000 can be formed from the digits 1, 3, 5, 7 and 9 without repetition? (3 marks)

A bag has 5 black and 6 red balls. In how many ways can 2 black and 3 red balls be selected? (3 marks)

Read the passage and answer the questions. A website needs 4-character passwords made only of the 26 capital letters. (i) How many passwords are possible with repetition? (ii) How many without repetition? (iii) Which principle of counting is used? (5 marks)

Read the passage and answer the questions. A shelf holds 6 different maths books and 4 different physics books. (i) In how many ways can all 10 books be arranged? (ii) In how many ways if the maths books stay together? (iii) Why is 6! multiplied in part (ii)? (5 marks)

Read the passage and answer the questions. A test has two parts of 5 questions each. A student must answer 7 questions with at least 3 from each part. (i) List the possible splits between the two parts. (ii) Find the number of ways for each split. (iii) Find the total number of ways. (5 marks)

Read the passage and answer the questions. A town issues vehicle plates with 2 letters followed by 3 digits. (i) How many plates are possible with repetition? (ii) How many with no repeated letter or digit? (iii) How many plates start with the letter A, with repetition allowed? (5 marks)

Read the passage and answer the questions. A pizza shop offers 8 different toppings. (i) In how many ways can a customer choose 3 toppings? (ii) Show that choosing 5 toppings gives the same number. (iii) How many 3-topping choices include mushrooms? (5 marks)

Derive the formula nPr = n!/(n - r)! for the number of permutations of n different objects taken r at a time. (6 marks)

Derive nCr = n!/(r!(n - r)!) and prove that nCr + nC(r - 1) = (n + 1)Cr. (6 marks)

Explain permutations when all the objects are not distinct, with the example of the word ALLAHABAD. (6 marks)

What is the number of ways of choosing 4 cards from a pack of 52? In how many of these are (i) all four cards red (ii) all four cards face cards? (6 marks)

In how many ways can a team of 3 boys and 3 girls be chosen from 5 boys and 4 girls? Explain the use of the multiplication principle in this problem. (6 marks)