Question

1) A lotto urn contains 3 balls: R(red), G(green), B(blue). How many 4-draw permutations are there if, after each draw, the ball is returned to the urn? Repeats are necessary since we make more draws than there are balls in the urn, and order is important and RBGB is considered a different draw from BRGB. PERMUTATION with REPETITION.

2) A lotto urn contains 3 balls: R(red), G(green), B(blue). How many 4-draw combinations are there if, after each draw, the ball is returned to the urn? Repeats are necessary since we make more draws than there are balls in the urn, but order is unimportant and RBGB is considered the same draw as BRGB. COMBINATION with REPETITION.

3) A lotto urn contains 7 balls: R(red), O(orange), Y(yellow), G(green), Blue(blue), I(indigo), V(violet). How many 3-draw combinations are there? There are "no repeats" because the balls are not returned after a draw, but order is unimportant because RBG is considered the same draw as BRG. COMBINATION without REPETITION.

Answer 1

Explanation:

(1) Since repeats are allowed, each draw has 3 options (R, G, or B), and there are 4 draws. So the number of 4-draw permutations is 3^4 = 81.

(2) Again, each draw has 3 options, and there are 4 draws. However, since order is unimportant, we need to divide by the number of ways we can arrange 4 draws, which is 4! = 24. So the number of 4-draw combinations is (3^4)/4! = 81/24 = 3.375, which we can round up to 4.

(3) Since there are no repeats, the number of options for the first draw is 7, the number of options for the second draw is 6 (since one ball has already been drawn), and the number of options for the third draw is 5 (since two balls have already been drawn). However, order is unimportant, so we need to divide by the number of ways we can arrange 3 draws, which is 3! = 6. So the number of 3-draw combinations is (765)/3! = 35.