1. Permutation. The order matters (1st, 2nd, 3rd place). Number of ways = P(5,3) = 5 × 4 × 3 = 60.
2. Combination. The order does not matter when selecting types of fruit. Number of ways = C(10,3) = 10! / (3! × 7!) = 120.
3. Combination. The order does not matter when choosing books from a bin. Number of ways = C(20,4) = 20! / (4! × 16!) = 4845.
4. Permutation. The batting order implies a specific sequence, so order matters. Number of ways = P(20,20) = 20! (for the full lineup), but if just ordering any subset for positions, it’s still a permutation problem based on position assignment.
5. Permutation. Arranging all 7 distinct numbers without repetition: 7! = 5040.
6. Combination with repetition allowed. Since toppings can repeat and order doesn’t matter for pizza toppings, use stars and bars: C(10 + 4 - 1, 4) = C(13,4) = 715.
7. Combination. Choosing 2 different sodas from 10 where order doesn’t matter: C(10,2) = 45.
8. Permutation. Electing officers to distinct positions (president, vice president, secretary) means order matters. Number of ways = P(300,3) = 300 × 299 × 298 = 26,730,600.
9. Permutation with repetition. 4-letter arrangements from 7 letters, allowing repeats: 7^4 = 2401.
10. Combination. Choosing 5 players from 30 where order doesn’t matter: C(30,5) = 30! / (5! × 25!) = 142506.
Parent Tip: Review the logic above to help your child master the concept of combinations and permutations worksheet with answers.
