The number of ways of selecting 10 clerks from 27 male 17 female applicants if the selection is to consist of either all males or all females=$$^{27}C_{10}$$ + $$^{17}C_{10}$$
The number of ways to select 10 clerks from 27 male $$=\ ^{27}C_{10}$$
The number of ways to select 10 clerks from 17 female $$=\ ^{17}C_{10}$$
This is either or condition so We will add the obtained number of ways
Such that, Total number of ways $$=\ ^{27}C_{10}+\ ^{17}C_{10}$$
From $$6$$ different novels and $$3$$ different dictionaries, $$4$$ novels and $$1$$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is
In a high school, a committee has to be formed from a group of $$6$$ boys $$M_{1}, M_{2}, M_{3}, M_{4}, M_{5}, M_{6}$$ and $$5$$ girls $$G_{1}, G_{2}, G_{3}, G_{4}, G_{5}$$. (i) Let $$\alpha_{1}$$ be the total number of ways in which the committee can be formed such that the committee has $$5$$ members, having exactly $$3$$ boys and $$2$$ girls. (ii) Let $$\alpha_{2}$$ be the total number of ways in which the committee can be formed such that the committee has at least $$2$$ members, and having an equal number of boys and girls. (iii) Let $$\alpha_{3}$$ be the total number of ways in which the committee can be formed such that the committee has $$5$$ members, at least $$2$$ of them being girls. (iv) Let $$\alpha_{4}$$ be the total number of ways in which the committee can be formed such that the committee has $$4$$ members, having at least $$2$$ girls and such that both $$M_{1}$$ and $$G_{1}$$ are NOT in the committee together. LIST - I LIST - II P. The value of $$\alpha_{1}$$ is $$1. 136$$ Q. The value of $$\alpha_{2}$$ is $$2. 189$$ R. The value of $$\alpha_{3}$$ is $$3. 192$$ S. The value of $$\alpha_{4}$$ is $$4. 200$$ $$5. 381$$ $$6. 461$$ The correct option is
Number of ways of selecting three squares on a chessboard so that all the three be on a diagonal line of the board or parallel to it is
Two teams are to play a series of five matches between them. A match ends in a win, loss or draw for a team. A number of people forecast the result of each match and no two people make the same forecast for the series of matches. The smallest group of people in which one person forecasts correctly for all the matches will contain $$n$$ people, where $$n$$ is
There are $$n$$ distinct white and $$n$$ distinct black balls. If the number of ways of arranging them in a row so that neighboring balls are of different colors is $$1152$$ then find the value of $$'n'$$.
Fifteen identical balls have to be put in five different boxes. Each box can contain any number of balls. The total number of ways of putting the balls into the boxes so that each box contains at least two balls is equal to
(a) A committee of 12 is to be formed from 9 women and 8 men. In how many ways this can be done if at least five women have to be included in a committee? In how many of these committees (i) the women are in majority (ii) the' men are in majority? (b) Out of 10 persons (6 males, 4 females), a committee of 5 is formed. p = number of such committees which include at least one lady. q = number of such committees which include at least two men. Find the ratio p:q.
A candidate is required to answer 7 out of 15 questions which are divided into three groups A, B, C each containing 4, 5, 6 questions respectively. He is required to select at least 2 questions from each group. In how many ways can he make up his choice?
A question paper consists of three sections A, B, C having 6,4,3 questions respectively. A student has the freedom to answer any number of questions but at least one question from each section is compulsory. In how many ways can the paper be attempted by the student?
930 Deepawali greeting cards are exchanged amongst the students of a class. If every student sends a card to every other student then what is the number of students in the class?