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Total number of words that can be formed using all letters of the word 'BRIJESH' that neither begins with 'I' nor ends with ' \(\mathrm{B}^{\prime}\) is equal to a. 3720 b. 4920 c. 3600 d. 4800

Total number less than \(3 \times 10^{8}\) and can be formed using the digits \(1,2,3\) is equal to a. \(\frac{1}{2}\left(3^{9}+4 \times 3^{8}\right)\) b. \(\frac{1}{2}\left(3^{9}-3\right)\) c. \(\frac{1}{2}\left(7 \times 3^{8}-3\right)\) d. \(\frac{1}{2}\left(3^{9}-3+3^{8}\right)\)

The number of ways of arranging \(m\) positive and \(n(

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 a. 81 b. 243 c. 486 d. none of these

In a group of 13 cricket players, four are bowlers. Find out in how many ways can they form a cricket team of 11 players in which at least 2 bowlers are included. a. 55 b. 72 c. 78 d. None of these

The number of ways in which we can distribute \(m n\) students equally among \(m\) sections is given by a. \(\frac{(m n) !}{n !}\) b. \(\frac{(m n) !}{(n !)^{m}}\) c. \(\frac{(m n) !}{m ! n !}\) d. \((m n)^{m}\)