A polynomial is defined as an expression that contains constants and variables which are connected together by the various mathematical operations. The important thing to note is that the exponent in a polynomial must be a non-negative integer and the polynomial cannot involve a division by a variable.
Based on this definition we can check the options one by one. Option A satisfies the criteria of a polynomial as exponent of the variable is 1 and there is no division by a variable.
Option B satisfies the definition of polynomial as all exponents are non-negative integers and there is no division by a variable.
Option C involves division by a variable, so it is not a polynomial.
Option D satisfies the definition of polynomial as all exponents are non-negative integers and there is no division by a variable.
Option E satisfies the definition of polynomial as all exponents are non-negative integers and there is no division by a variable.
Option F is not a polynomial as it has a variable in the exponent. The exponents can only be the non-negative integers.
5*4 for the male roles 6*5 for the female roles after they are assigned 7*6 for the either gender 20+30+42 =92 total ways or 20*30*42= 25200 total ways
