Combination

There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that:

The fastest computer gets the toughest job and the slowest computer gets the easiest job.
Every computer gets at least one job.

The number of ways in which this can be done is ___________.

The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L's are indistinguishable, is ______.

The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is ______________.

The number of 4 digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set {1, 2, 3} is____________.

The number of divisors of 2100 is _____ .

The number of bit strings of length 8 that will either start with 1 or end with 00 is?

The number of distinct positive integral factors of 2014 is ____

A pennant is a sequence of numbers, each number being 1 or 2. An n-pennant is a sequence of numbers with sum equal to n. For example, (1,1,2) is a 4-pennant. The set of all possible 1- pennants is {(1)}, the set of all possible 2-pennants is {(2), (1,1)}and the set of all 3-pennants is {(2,1), (1,1,1), (1,2)}. Note that the pennant (1,2) is not the same as the pennant (2,1). The number of 10- pennants is _____.

There are 5 bags labelled 1 to 5. All the coins in a given bag have the same weight. Some bags have coins of weight 10 gm, others have coins of weight 11 gm. I pick 1, 2, 4, 8, 16 coins respectively from bags 1 to 5. Their total weight comes out to 323 gm. Then the product of the labels of the bags having 11 gm coins is ___.

In how many ways can b blue balls and r red balls be distributed in n distinct boxes?