A code word consisis of three letters of the English alphabet followed by two digits of the decimal system. If neither letter nor digit is repeated in any code word, the total number of code words is:
There are n straight lines in a plane in which no two are parallel and no three pass through the same point. Their points of intersection are joined. Show that the number of fresh lines thus introduced is
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The number of signals that, can be generated by using 6 differently colored flags, when any number of them may be hoisted at a time is:
If n is even and nC0 < nC1 < nC2 < .... nCr > nCr+1 > nCr-2 > .... nCn Then r = ?
The principal wants to arrange 5 students on the platform such that the boy SALIM occupies the second position and such that the girl SITA is always adjacent to the girl RITA. How many such arrangement are possible:?
For a set of five true/false questions, no student has written all correct answers, and no students have given the same sequence of answer. What is the maximum number of students in the class, for this to be possible?
In a certain test, αi, students gave wrong answers to at least i questions, where i = 1,2,3.4...k. No student gave more than k wrong answers the total number of wrong answers given is :
In how many ways can 10 balls be divided between two boys. One receiving two and the other eight balls?
Three men have 4 coats, 5 waist coat and 6 caps. In how many ways can they wear them?
How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digit occupy even positions?
How many numbers greater than 10 lacs be formed from 2,3,0,3,4,2,3.
Five digil number divisible by 9 are to be formed by using the digit 0,1,2,3,4,7,8 (without repetition). The total number of such numbers is equal to
Even numbers are formed with three digits such that if 5 is one of the digit then 7 is the next digit. The number of such numbers is (repetition is allowed).
The number of divisiors of 9600 including 1 and 9600 is
Out of 5 computers scientist and 7 mathematician a committee consisting of 2 computer scientists and 3 mathematicians is to be formed. The number of ways in which this can be done if any computer scientists and any mathematician can be included is :
If (rn ≠ 0) is positive integer, then the number of positive integeral solution of x + y + z + t = m is
Number of diagonals in a convex n sided polygon is :
In a certain town the streets are arranged like the lines of a chess board. There are 6 street running north and south ard 10 running east and west. These number of ways in which a man can go N.W. corner to the S.E. corner covering the shortest possible distance in each case is :
We have 5 locks and 5 keys to them. How many trails must we make in the least favourable cases to establish the correspondence between the locks and the keys?
25 points, no 3 co-linear are given in a plane. How many triangles do they determine?
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