Permutations and Combinations — Flashcards
ICSE · Class 11 · Mathematics
28 flashcards for Permutations and Combinations (ICSE Class 11 Mathematics) to test yourself on key terms and facts. Sample: "Evaluate: 6!"
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Evaluate: 6!
Answer
Step 1: Use the factorial rule: n! = n x (n-1) x (n-2) x ... x 2 x 1. Step 2: 6! = 6 x 5 x 4 x 3 x 2 x 1. Step 3: Multiply: 6 x 5 = 30, 30 x 4 = 120, 120 x 3 = 360, 360 x 2 = 720. Answer: 6! = 720.
Why is 0! taken as 1?
Answer
0! is fixed by convention as 1. Reason: This keeps formulas like nPn = n! valid when r = n. Check: nPn = n! / (n-n)! = n! / 0!. For this to equal n!, 0! must be 1. Answer: 0! = 1 by convention.
Evaluate: 7! / 4!
Answer
Step 1: Expand only the larger factorial. 7! / 4! = (7 x 6 x 5 x 4!) / 4! Step 2: Cancel 4!. Step 3: Multiply the remaining numbers. 7 x 6 x 5 = 210 Answer: 7! / 4! = 210.
Check whether 3! + 2! = 5!
Answer
Step 1: Find 3! = 6 and 2! = 2. Step 2: Add: 3! + 2! = 6 + 2 = 8. Step 3: Find 5! = 120. Step 4: Compare 8 and 120. Answer: 3! + 2! is not equal to 5!. Common mistake: adding factorials as if they com…
How many ways can 3 different flavour choices and 2 different topping choices be combined for a one-scoop ice cream with one topping?
Answer
Step 1: Choose a flavour in 3 ways. Step 2: Choose a topping in 2 ways. Step 3: Use multiplication principle because both choices happen in succession. Total ways = 3 x 2 = 6. Answer: 6 ways.
A laptop store has 8 models of brand A and 6 models of brand B. How many choices are there if one laptop is to be chosen from either brand?
Answer
Step 1: The choice is brand A or brand B. Step 2: Use addition principle for disjoint alternatives. Total choices = 8 + 6 = 14. Answer: 14 choices. Common mistake: using multiplication instead of addi…
How many 3-digit numbers can be formed from 1, 2, 3, 4 and 5 if repetition is allowed?
Answer
Step 1: Order matters, so the hundreds, tens, and ones places are filled separately. Step 2: Hundreds place = 5 choices. Step 3: Tens place = 5 choices. Step 4: Ones place = 5 choices. Step 5: Use mul…
Why are AB and BA different in permutations but the same in combinations?
Answer
In permutations, order matters. So AB and BA are two different arrangements. In combinations, order does not matter. So AB and BA represent the same selection. Example: choosing a chairman and vice-ch…
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