Permutations & Combinations
Permutation and Combination
star_batch_jee_advanced_2025
Grade 11
A dice is thrown 7 times. Find the number of possible outcomes if:
Step-by-Step Solution
Key Concept: The total number of outcomes for independent events is found by multiplying the number of possibilities for each event, giving $6^7$ for 7 dice throws.
When a dice is thrown 7 times, each throw is an independent event with 6 possible outcomes (1, 2, 3, 4, 5, or 6). By the fundamental counting principle, the total number of possible outcomes is the product of outcomes for each trial: $6 imes 6 imes 6 imes 6 imes 6 imes 6 imes 6 = 6^7$. Calculating: $6^7 = 279936$. This represents all possible sequences of 7 dice throws without any restrictions.
Correct Answer: [A-q] [B-s] [C-p] [D-r]