BooleanCountingFunction

BooleanCountingFunction[kmax, n] represents a Boolean function of n variables that gives True if at most kmax variables are True.

BooleanCountingFunction[{k}, n] represents a function that gives True if exactly k variables are True.

BooleanCountingFunction[{kmin, kmax}, n] represents a function that gives True if between kmin and kmax variables are True.

Examples

At most 2 of 4 variables true:

BooleanCountingFunction[2, 4][True, False, True, False]
(* True *)

Exactly 2 variables true:

BooleanCountingFunction[{2}, {a, b, c}]

Please visit the official Wolfram Language Reference for more details.