1.
If a 9-digit number is chosen at random what is the probability that at least two digits are the same?
Ans: (10^9-10!)/10^9
2.
How many sequences are there of 26 letters with each of the letters of the alphabet appearing exactly once and that do not contain the sequences of letters ABCD, ZYXW, MNOP, or SNOT?
Ans: 26! - 4(23!) +6(20!) - 4(17!) +14!
3.
There are 100 pennies, how many ways are there of distributing them to 5 different people(i.e. each person may or may not get some of these pennies)? How many ways are there of distributing these pennies so that each person gets at least 5 pennies each?
Ans: 104C4 , 79C4
4.
How many ways are there of rolling a sided die 10 times in a sequence such that all 6 faces appear at least once?
Ans: 6^4(6!) (10C6)有notes,但不明*6^4,coz 10-6=4(repeat). 10C6=whole*
5.
If more than half of the integers from {1,2,.....2n} are selected, then some two of the selected integers have the property that one divides the other.
Ans: {1,2}{2,4}{3,6}......{n,2n} . n is the pigeon, so by pigeon-hole,..........點解要用....{n,2n}?
請幫我解一解釋, 和告訴我有什麽訣竅,要怎麼才能夠輕易地算discrete math??我最差的就是這個了..TT 謝謝!!!
更新1:
why you are so good at math?do u hav any way to share how can i improve my discrete math and the others???
