1. Permutation. The order matters (1st, 2nd, 3rd place). Number of ways: P(5,3) = 5! / (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!) = (10 × 9 × 8) / (3 × 2 × 1) = 120.
3. Combination. The order does not matter when choosing books from a bin. Number of ways: C(20,4) = 20! / (4! × 16!) = (20 × 19 × 18 × 17) / (4 × 3 × 2 × 1) = 4845.
4. Permutation. The batting order implies a specific sequence, so order matters. Number of ways: P(20,20) = 20! (the full factorial of 20).
5. Permutation. Arranging distinct numbers where order matters and no repeats are allowed. Number of ways: 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.
6. Combination with repetition. Toppings can be repeated, and the order of selection doesn't matter for the pizza. Number of ways: C(10 + 4 - 1, 4) = C(13,4) = 13! / (4! × 9!) = (13 × 12 × 11 × 10) / (4 × 3 × 2 × 1) = 715.
7. Combination. Joseph wants 2 different types, and the order he picks them doesn't matter for the combination. Number of ways: C(10,2) = 10! / (2! × 8!) = (10 × 9) / (2 × 1) = 45.
8. Permutation. The positions (president, vice president, secretary) are distinct, so order matters. Number of ways: P(300,3) = 300 × 299 × 298 = 26,730,600.
9. Permutation with repetition. Letters can be repeated, and order matters for arrangements. Number of ways: 7^4 = 7 × 7 × 7 × 7 = 2401.
10. Combination. Choosing players for a team where the order of selection doesn't matter. Number of ways: C(30,5) = 30! / (5! × 25!) = (30 × 29 × 28 × 27 × 26) / (5 × 4 × 3 × 2 × 1) = 142506.
Parent Tip: Review the logic above to help your child master the concept of permutation combination worksheet.
