Consider the set x = { 1 , 2 , 3 , 4 , 5 } x={1,2,3,4,5} and suppose you have two holes. also suppose that you have 10 10 pigeons: the 2 2-element subsets of x . x. can you put these 10 10 pigeons into the two holes in a way that there is no 3 3-element subset s = { a , b , c } ⊂ x s={a, b,c}⊂x for which all pigeons from s s go in the same hole? then answer the same question if x = { 1 , 2 , 3 , 4 , 5 , 6 } x={1,2,3,4,5,6} with 15 = c ( 6 , 2 ) 15=c(6,2) pigeons.

Leslie started last week with $1200 in her checking account. during the week, she wrote the checks below. trans typ./ check no. date description of transaction payment/ debit deposit/ credit (+) balance 1,200 00 324 10/6 miller's food market 45.87 45 87 groceries 1,154 13 325 10/7 cyber center computer outlet 218.59 218 59 monitor 935 54 326 10/9 sandy's beauty salon 30.00 30 00 haircut and styling 900 59 deposit 10/10 paycheck 621.33 621 33 1,621 92 evaluate leslie's check register. a. leslie did a good job. everything is correct. b. the final balance is wrong; she did not add everything correctly. c. leslie should have written debit instead of deposit for the transaction type. d. leslie switched the debit and credit columns.