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There are 3 books of mathematics, 4 of science, and 5 of literature.How many different collections can be made such that each collection consistsofone book of each subject,at least one book of each subject,at least one book of literature. |
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Answer» (i) One book of each subject is selected. So, number of ways of selections `=.^(3)C_(1)xx .^(4)C_(1)xx .^(5)C_(1)` `=3xx4xx5=60` (ii) At least one book of each subject is selected. Number of ways of ways of selection of at least one mathematics book `=3^(3)-1=7` Number of ways of selection of at least one science book `=2^(4)-1=15` Number of ways of selection of at least one literature book `=2^(5)-1=31` So, total number of ways of selection `=7xx15xx31=3255` (iii) At least one book of literature is selected. So, we can select any number of mathematics and science books including zero selection. So, number of ways of selection `=2^(3)xx2^(4)xx(2^(5)-1)` `=128xx31=3968` |
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