The probability that in a random arrangement of the letters of the word 'UNIVERSITY', the two 'I's do not come together is

The logical statement

$$ [\sim(\sim p \vee q) \vee(p \wedge r) \wedge(\sim q \wedge r)] $$

is equivalent to

The L.P.P. , minimize $z=30 x+20 y, x+y \leq 8$, $x+2 y \geq 4,6 x+4 y \geq 12, x \geqslant 0, y \geqslant 0$ has

If the distance of the point $\mathrm{P}(1,-2,1)$ from the plane $x+2 y-2 z=\alpha$, where $\alpha>0$ is 5 units, then the foot of the perpendicular from P to the plane is