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In a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?
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Suppose \[A_1 , A_2 , . . . , A_{30}\] are thirty sets each having 5 elements and \[B_1 , B_2 , . . . , B_n\] are n sets each with 3 elements. Let \[\cup^{30}_{i = 1} A_i = \cup^n_{j = 1} B_j = S\] and each element of S belong to exactly 10 of the \[A_i 's\]and exactly 9 of the\[B_j 's\] then n is equal to
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Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of m and n are respectively
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From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
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How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
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In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
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In how many ways can a football team of 11 players be selected from 16 players? How many of these will
include 2 particular players?
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In how many ways can a football team of 11 players be selected from 16 players? How many of these will
exclude 2 particular players?
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There are 10 professors and 20 students out of whom a committee of 2 professors 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 professor is included.
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There are 10 professors and 20 students out of whom a committee of 2 professors 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 included.
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There are 10 professors and 20 students out of whom a committee of 2 professors 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.
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How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
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From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
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How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
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How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
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How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
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From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
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From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
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A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?
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A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions?
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