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In a certain an algebraical exercise boo...

In a certain an algebraical exercise book there and 4 examples on arithmetical progression, 5 examples on permutation and combination, and 6 examples on binomial theorem. Find the number of ways a teacher can select or his pupils at least one but not more than 2 examples from each of these sets.

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Number of ways teacher can select examples from arithmetic progression `=(.^(4)C_(1)+ .^(4)C_(2))`
Number of ways teacher can select examples from permutation and combination `=(.^(5)C_(1) + .^(5)C_(2))`
Number of ways teacher can select examples from binomial theorem `=(.^(6)C_(1)+ .^(6)C_(2))`
Hence, total number of ways `=(.^(4)C_(1)+ .^(4)C_(2))(.^(5)C_(1)+ .^(5)C_(2))(.^(6)C_(1)+ .^(6)C_(2))`
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