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There are (p+ q) different books on different topics in Mathematics. (p  q) If L = the number of ways in which these books are distributed between two students X and Y such that X get p books and Y gets q books. M = The number of ways in which these books are distributed between two students X and Y such that one of them gets p books and another gets q books. N = The number of ways in which these books are divided into two groups of p books and q books then?
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There are (p+ q) different books on different topics in Mathematics. (...

Total number of ways = (p+q)!  /  p! q! = L
Total number of ways = (p+q)!  / p! q! q! =M
Total number of ways =(p+q)!  /  p! q! � q! =N
L / 2 = M =N
L= 2 M = 2N correct answer 
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There are (p+ q) different books on different topics in Mathematics. (...
Solution:

  • Finding L: The number of ways to distribute p books to X and q books to Y is given by the formula for combinations. Thus, L = (p+q)Cp.

  • Finding M: There are two ways to approach this problem.

    • Method 1: Either X gets p and Y gets q or X gets q and Y gets p. Therefore, M = 2(pq).

    • Method 2: We can use the formula for total number of ways to distribute p+q books to two students. Thus, M = 2^(p+q-1) - L.



  • Finding N: We need to divide the books into two groups of p and q books each. We can select p books out of p+q books in (p+q)Cp ways. After selecting these p books, the remaining q books will automatically form the second group of q books. Thus, N = (p+q)Cp.


Therefore, the solutions are:

  • L = (p+q)Cp

  • M = 2(pq) or M = 2^(p+q-1) - L

  • N = (p+q)Cp

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There are (p+ q) different books on different topics in Mathematics. (p  q) If L = the number of ways in which these books are distributed between two students X and Y such that X get p books and Y gets q books. M = The number of ways in which these books are distributed between two students X and Y such that one of them gets p books and another gets q books. N = The number of ways in which these books are divided into two groups of p books and q books then?
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