Permutations and Combinations
Telangana Open School (TOSS) · Class 12 · Mathematics
Flashcards for Permutations and Combinations — Telangana Open School (TOSS) Class 12 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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How many 3-digit numbers can be formed using digits 1, 2, 3, 4, 5 without repetition?
Answer
Step 1: Choose digit for hundreds place → 5 options.<br>Step 2: Choose digit for tens place → 4 remaining options.<br>Step 3: Choose digit for units place → 3 remaining options.<br>Using Fundamental P…
In how many ways can 6 books be arranged on a shelf?
Answer
This is a permutation of 6 distinct objects.<br>Formula: n! = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.<br>Answer: 720 ways.
Evaluate 5P3.
Answer
Formula: nPr = n! / (n−r)!<br>Here, n = 5, r = 3.<br>5P3 = 5! / (5−3)! = (5×4×3×2×1) / (2×1) = 120 / 2 = 60.<br>Answer: 60.
There are 4 trains from A to B and 3 from B to C. In how many ways can one go from A to C?
Answer
Using Fundamental Principle of Counting:<br>First event (A to B): 4 ways.<br>Second event (B to C): 3 ways.<br>Total ways = 4 × 3 = 12.<br>Answer: 12 ways.
How many 4-letter palindromes can be formed using English alphabets?
Answer
A palindrome reads same forwards and backwards.<br>For 4 letters: First 2 letters determine the last 2.<br>1st letter: 26 choices.<br>2nd letter: 26 choices.<br>3rd = 2nd, 4th = 1st → no choice.<br>To…
In how many ways can 3 prizes be distributed among 10 students if no student gets more than one prize?
Answer
This is arranging 3 out of 10 students.<br>Order matters → permutation.<br>10P3 = 10 × 9 × 8 = 720.<br>Answer: 720 ways.
How many 4-digit numbers can be formed using digits 1, 2, 3, 4, 5, 6 if digits can repeat?
Answer
Each digit place (thousands, hundreds, tens, units) can be filled independently.<br>Thousands: 6 choices (1–6).<br>Hundreds: 6 choices.<br>Tens: 6 choices.<br>Units: 6 choices.<br>Total = 6 × 6 × 6 × …
Evaluate 7! / 5!.
Answer
7! = 7×6×5!, so 7! / 5! = 7×6 = 42.<br>Answer: 42.
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