Find the value of the constant k given the probability mass function P(X=x) = k(7−x)(x+1) for x = 0, 1, 2, 3, 4, 5, 6.

Step 1: Solve Question 5 (a) - The value of the constant $k$.
The sum of probabilities for a discrete random variable must equal 1.
The probability mass function is $P(X=x) = k(7-x)(x+1)$ for $x = 0, 1, 2, 3, 4, 5, 6$.
Calculate $P(X=x)$ for each value of $x$:
$P(X=0) = k(7-0)(0+1) = 7k$
$P(X=1) = k(7-1)(1+1) = k(6)(2) = 12k$
$P(X=2)