Commerce (English Medium) Class 11 - CBSE Question Bank Solutions

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has no girls

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least one boy and one girl

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least three girls.

If ⁿC₁₂ = ⁿC₈, then n is equal to ______.

Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.

Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.

The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is ______.

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is ______.

The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is ______.

The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is ______.

Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is ______.

¹⁵C₈ + ¹⁵C₉ – ¹⁵C₆ – ¹⁵C₇ = ______.

Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ______.

In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship is ______.

The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ______.

A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.

A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ______.

There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is ¹²C₂ – ⁵C₂.

If some or all of n objects are taken at a time, the number of combinations is 2ⁿ – 1.

Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is `(11!)/(5!6!) (9!)(9!)`.