Number of Boolean function possible

Question

Number of boolean function with 3 boolean variable such that the function contain exactly 2 or 7 min term in their canonical SOP?

Please explain the logic!

Comments

36 maximum functions are possible

Answer 1

If we draw the truth table with 3 variables, then 2³ combinations are possible. The function needs to produce exactly 2 minterms, so $\binom{2^{3}}{2}$ functions ar possible.

Similarly, to have 7 minterms, $\binom{2^{3}}{7}$ functions are possible.

Using addition rule of counting, $\binom{2^{3}}{2} + \binom{2^{3}}{7}$ functions are possible.

Comments

thanks brother, so it means that any 2 min-term in final function, I thouht 2 or 7 means (010 or 111 only)

so they are, (X'Y'Z'+XYZ),(XY'Z'+XYZ),etc. right?

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Yes any 2 minterms means any two out of these eight minterms.

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Thanks bro!