What is the mathematical probability that no pair of male individuals sits adjacently in a photograph containing 5 female individuals and 2 male individuals?
Show answer Hide answer
Answer: D. 5/7
Explanation
Arranging five female individuals creates six potential seating gaps where male individuals can be placed safely. Selecting two distinct gaps out of the six available positions ensures that no two males sit together. Calculating the combinatorial ratio of valid seating arrangements yields a final probability of five-sevenths. Combinatorics provides mathematical tools to count favorable seating arrangements among distinct groups of individuals. The total number of unconstrained ways to arrange seven individuals in a line equals factorial of seven. Conditional probabilities restrict sample spaces to configurations that satisfy specific adjacency constraints successfully.
Event planners use combinatorial probability models to design seating arrangements for diplomatic banquets and conferences. Statistical mechanics applies similar combinatorial exclusion principles to analyze particle distributions in quantum states. Educational software developers incorporate permutation and combination puzzles to test student logical reasoning skills. Option A suggests one over twenty-one which severely underestimates the likelihood of avoiding male adjacency. Option B proposes four over sevenths which miscounts the favorable combinatorial placement configurations. Option C implies two over sevenths which represents an incorrect ratio of valid seating gaps.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. Two inlet spigots fill a basin in 10 minutes and 15 minutes individually, and when combined with an open drain pipe, the basin fills in 18 minutes. How long does the drain pipe take to empty the completely filled basin?
Show answer Hide answer
Answer: D. 9 min
The combined flow rate of the two inlet pipes is found by summing their individual rates. Subtracting the net combined filling rate of eighteen minutes from the inlet rate gives the drain rate. Inverting the resulting dr...
Q2. A hexahedron possesses a surface area of 726m2; determine its volumetric capacity.
Show answer Hide answer
Answer: B. 1331 m3
A hexahedron, or cube, has six identical square faces, making each face area equal to 726 divided by six, or 121 square meters. Taking the square root of 121 gives an edge length of 11 meters for the cube. Cubing the edg...
Q3. What is the statistical likelihood of selecting two club suits from a standard thoroughly shuffled 52-card deck?
Show answer Hide answer
Answer: B. 1/17
The probability of drawing the first club suit from a standard deck is thirteen over fifty two. The probability of drawing a second club from the remaining cards is twelve over fifty one. Multiplying these two independen...
Q4. What is the perimeter measurement of a square land plot whose diagonal spans 8√2?
Show answer Hide answer
Answer: B. 32 m
The diagonal of a square equals the side length multiplied by the square root of two. Dividing the given diagonal by the square root of two extracts the base side length. Multiplying the single side length by four calcul...
Q5. What financial return does Kiran accumulate by depositing Rs.8000 at a 10% annual compound interest rate over a span of two years, compounded yearly?
Show answer Hide answer
Answer: E. None of these
Applying the compound interest formula to Rs. 8000 at 10 percent for two years multiplies the principal by 1.1 squared. Calculating this product yields a final compound amount of Rs. 9680 at the end of the two-year perio...
Q6. A rectangular yard with side lengths in a 4:3 proportion incurs a paving expense of Rs.600 at 50 p per m2; calculate the length of the yard's diagonal.
Show answer Hide answer
Answer: D. 50 m
The total area is calculated by dividing the paving expense by the cost per square meter. Using side lengths four x and three x yields twelve x squared equal to twelve hundred. Solving for x gives ten, making the side di...