Tamil Nadu Board of Secondary EducationHSC Commerce Class 11

The number of 3 letter words that can be formed from the letters of the word ‘NUMBER’ when the repetition is allowed are: - Business Mathematics and Statistics


The number of 3 letter words that can be formed from the letters of the word ‘NUMBER’ when the repetition is allowed are:


  • 206

  • 133

  • 216

  • 300




Concept: Combinations
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Chapter 2: Algebra - Exercise 2.7 [Page 46]


If four dice are rolled, find the number of possible outcomes in which atleast one die shows 2.

There are 18 guests at a dinner party. They have to sit 9 guests on either side of a long table, three particular persons decide to sit on one side and two others on the other side. In how many ways can the guests to be seated?

If a polygon has 44 diagonals, find the number of its sides.

A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this can be done when

  1. atleast two ladies are included.
  2. atmost two ladies are included.

How many code symbols can be formed using 5 out of 6 letters A, B, C, D, E, F so that the letters

  1. cannot be repeated
  2. can be repeated
  3. cannot be repeated but must begin with E
  4. cannot be repeated but end with CAB.

From 20 raffle tickets in a hat, four tickets are to be selected in order. The holder of the first ticket wins a car, the second a motor cycle, the third a bicycle and the fourth a skateboard. In how many different ways can these prizes be awarded?

If nC3 = nC2 then the value of nC4 is:

The number of ways selecting 4 players out of 5 is

The number of diagonals in a polygon of n sides is equal to

Thirteen guests have participated in a dinner. The number of handshakes that happened in the dinner is:

If nC12 = nC9 find 21Cn

If nPr = 720 and nCr = 120, find n, r

Prove that `""^35"C"_5 + sum_("r" = 0)^4 ""^((39 - "r"))"C"_4` = 40C5

If `""^(("n" + 1))"C"_8 : ""^(("n" - 3))"P"_4` = 57 : 16, find the value of n

A Kabaddi coach has 14 players ready to play. How many different teams of 7 players could the coach put on the court?

In a parking lot one hundred, one-year-old cars, are parked. Out of them five are to be chosen at random for to check its pollution devices. How many different set of five cars can be chosen?

How many ways can a team of 3 boys,2 girls and 1 transgender be selected from 5 boys, 4 girls and 2 transgenders?

Find the total number of subsets of a set with
[Hint: nC0 + nC1 + nC2 + ... + nCn = 2n] 4 elements

There are 5 teachers and 20 students. Out of them a committee of 2 teachers and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees a particular student is excluded?

In an examination a student has to answer 5 questions, out of 9 questions in which 2 are compulsory. In how many ways a student can answer the questions?

Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly three aces in each combination

How many triangles can be formed by 15 points, in which 7 of them lie on one line and the remaining 8 on another parallel line?

There are 11 points in a plane. No three of these lies in the same straight line except 4 points, which are collinear. Find, the number of straight lines that can be obtained from the pairs of these points?

Choose the correct alternative:
If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then the total number of points of intersection are

Choose the correct alternative:
In 2nC3 : nC3 = 11 : 1 then

Choose the correct alternative:
`""^(("n" - 1))"C"_"r" + ""^(("n" - 1))"C"_(("r" - 1))` is

Choose the correct alternative:
If nC4nC5nC6 are in AP the value of n can be


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