Q1
By the fundamental principle of counting, if one task can be done in 3 ways and another in 4 ways, both tasks together can be done in:
📝 SolutionThe fundamental (multiplication) principle of counting says if one event has $m$ outcomes and another independent event has $n$ outcomes, together they have $m \times n$ outcomes: $3 \times 4 = 12$.
Q2
The value of $5!$ is:
📝 Solution$5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$.
Q3
$^nP_r$ is defined as:
📝 SolutionThe number of permutations of $n$ distinct things taken $r$ at a time is $^nP_r = \frac{n!}{(n-r)!}$.
Q4
The value of $^5P_2$ is:
📝 Solution$^5P_2 = \frac{5!}{(5-2)!} = \frac{5!}{3!} = 5 \times 4 = 20$.
Q5
$^nC_r$ is defined as:
📝 SolutionThe number of combinations of $n$ things taken $r$ at a time is $^nC_r = \frac{n!}{r!(n-r)!}$, which counts selections without regard to order.
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Class 11 · Maths
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