Permutation and Combination Test 1

 In how many ways a kabaddi team of 6 players can be made from 12 players if a particular player is never chosen?

In how many ways can 5 boys and 7 girls be arranged in a row so that no two boys are together?

3 Girls and 4 boys are to be seated in a row on 7 chairs in such a way that all the three girls always sit together. In how many different ways can it be done?

 In how many ways we can arrange the letters of the word “ARRAGEET”?

A deck of 52 cards is taken. From this, 4 cards are to be chosen such that exactly two of them are hearts and exactly two of them are kings. In how many ways can this be done?

 In how many ways the letters of word FACETIOUS can be arranged so that the first three letters are in dictionary order?

In how many ways can the letters of word AVERAGE be rearranged so that all the vowels are together and all the consonants are together, but no two same letters are together?

 In how many ways can the letters of word CHAMPION be arranged so that no two vowels come together?

The number of words that can be made by rearranging the letters of the word ‘ANUPTA’ so that the even places are always occupied by consonants is

A jar contains 2 pink balls, 3 orange balls and 4 green balls. In how many ways can 3 balls be drawn from the jar, if at least one orange ball is to be included in the draw?

A school has two volleyball teams with eight players each. A new five – member team has to be selected from these two teams for an inter school competition. How many selections are possible?

In how many different ways can the letters of the word ‘BLOATING’ be arranged?

Quantity A: If ⁿC₂₁ = ⁿC₂₇, then ⁵⁰C_n = ?Quantity B: If ⁿP₄ = 1680, then ⁿC₃ = ?

Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers.

Quantity A∶ In how many different ways can the letters of the word PAINTER be arranged in such a way that the vowels occupy only the even positions?Quantity B∶ There are 12 points in a plane out of which 4 are collinear. Find the number of lines that can be formed from 12 points.

Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.

Quantity A: A three-digit number is formed using digits 1, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers?

Quantity B: A three-digit number is formed using digits 1, 8 and 7 without repeating any one of them. What is the sum of all such possible numbers?