Screening — RisingBrain

Sheets Domain Screening Courses Interview

Quant Aptitude

Probability and combinatorics

10 questions

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Probability & Combinatorics

1. The AND / OR Rule

AND → multiply ( $m \times n$ ).
OR → add ( $m + n$ ).

2. Permutation & Combination Patterns

Word with repeats (e.g. MISSISSIPPI): $\dfrac{n!}{p!\,q!\,r!}$
Circular (around a table): $(n-1)!$
Necklace / garland (clockwise = anticlockwise): $\dfrac{(n-1)!}{2}$
Handshakes / lines from $n$ points: $\dbinom{n}{2} = \dfrac{n(n-1)}{2}$
Diagonals of an $n$ -gon: $\dfrac{n(n-3)}{2}$
Select at least one from $n$ distinct items: $2^{n} - 1$

3. Probability

P(E) = \frac{\text{favourable outcomes}}{\text{total outcomes}}

Item	Quick facts
Coins	$n$ coins → $2^{n}$ outcomes
Dice	$n$ dice → $6^{n}$ outcomes; for two dice, sum 7 is likeliest (6 ways)

"At least one": $P(\text{at least one}) = 1 - P(\text{none})$ .
Without replacement (dependent): denominator drops each draw — e.g. $\dfrac{5}{12}\times\dfrac{4}{11}$ .