WPS PDF编辑试用1 How many 4-tuples are there in the relation {(a,b,c,d)l a,b,c,and d are positive integers withabcd 6)?(1 mark)2 How many strings of six lowercase letters from the English alphabet contain(4 mark)a)the letter a?b)the letters a and b?c)the letters a and b in consecutive positions with a preceding b,with all the letters distinct?d)the letters a and b,where a is somewhere to the left ofb in the string,with all the letters distinct?(Just give the formula,you don't have to compute the result)3 Show that given any set of 10 positive integers not exceeding 50 there exist at least two differentfive-element subsets of this set that have the same sum.(1 mark)5 Letn be a nonnegative integer.Find out the wrong one(or ones)among the following identitiesand correctit(or them).(1.5 mark)6 How many positive integers less than 1000 are divisible by exactly one of 7 and 11?(1 mark)Please write down your calculation process.