The number of ways in which 20 persons can sit on 8 chairs round a circular table is-

The number of numbers can be formed by taking any 2 digits from digits 6,7,8,9 and 3 digits from 1, 2, 3, 4, 5 is -

How many numbers consisting of 5 digits can be formed in which the digits 3,4 and 7 are used only once and the digit 5 is used twice-

The number of ways of distributing n prizes among n boys when any of the student does not get all the prizes is-

If the line is a tangent to the parabola then k=

The number of ways in which n prizes can be distributed among n students when each student is eligible to get any number of prizes is-

In how many ways can six different rings be wear in four fingers?

It is important to note that we have used a basic fundamental principle of counting to find the total ways. Also, it is important to notice that each ring has 4 ways as it has not been given that each finger must have at least one ring. So, there can be 6 rings in a finger alone and remaining all the fingers empty.

How many signals can be given by means of 10 different flags when at a time 4 flags are used, one above the other?

The number of ways in which three persons can dress themselves when they have 4 shirts. 5 pants and 6 hats between them, is-

Eleven animals of a circus have to be placed in eleven cages, one in each cage. If four of the cages are too small for six of the animals, the number of ways of caging the animals is-

Eight chairs are numbered from 1 to 8. Two women and three men wish to occupy one chair each. First women choose the chairs from amongst the chairs marked 1 to 4; and then the men select the chairs from the remaining. The number of possible arrangements is-

It is important to note that we have used a fact that  = . This can be understood as we know that  = and  =   . So, substituting this we have  =  . 

A tea party is arranged of 16 persons along two sides of a long table with 8 chairs on each side. 4 men wish to sit on one particular side and 2 on the other side. In how many ways can they be seated ?

Whenever we face such types of problems the key point is to make special arrangements for the people who are in need of it, then arrange the remaining. Now combination comes with permutation as there are possibilities of these 8 people sitting on one side to rearrange. Thus this concept into consideration, to get through the answer.

If ^(m+n) P₂ = 56 and ^m–nP₂ = 12 then (m, n) equals-

A thin uniform annular disc (see figure) of mass has outer radius and inner radius . The work required to take a unit mass from point on its axis to infinity is

The two bodies of mass and respectively are tied to the ends of a massless string, which passes over a light and frictionless pulley. The masses are initially at rest and the released. Then acceleration of the centre of mass of the system is

If  to  terms,   terms, , then