Use pigeonhole principle to prove the following (need to identify pigeons/objects and pigeonholes/boxes): a. how many cards must be drawn from a standard 52-card deck to guarantee 2 cards of the same suit? note that there are 4 suits b. prove that if four numbers are chosen from the set {1, 2, 3, 4,5,6), at least one pair must add up to 7.

Step-by-step explanation:

a. The pidgeons/objects here are the cards and the pigeonholes/boxes here are the suits. We are trying to draw cards/pidgeon that have the same suits/pidgeonholes. Since there are 4 different suits, we need to draw at least 5 cards to guarantee 2 cards of the same suit.

b. Let there be 3 holes, which represent 3 pairs of number with sum equals to 7. They are:

- {1,6} as 1 + 6 = 7

- {2,5} as 2 + 5 = 7

- {3,4} as 3 + 4 = 7

You can see that if we pick randomly 4 numbers, we will always end up with 2 numbers in the same hole, which means there will be at least a pair and add up to 7.

c. side angle side. u shares the same sides

it's 100

step-by-step explanation:

22, 28, 34, 40, 46

b)   f(n) = 6n + 16

  n = what is the number of the row ( 22 would be row 1) so if we replaced n with 1, we would get 22

c)   the  14th  row will have 100 seats

(1)   (2)   (3)   (4)   (5)   (6)   (7)   (8)   (9)   (10) (11) (12) (13) (14)

22 | 28 | 34 | 40 | 46 | 52 | 58 | 64 | 70 | 76 | 82 | 88 | 94 | 100

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