Important Questions of Permutation and combination ANIL VERMA Director GIITJEE Chandigarh
Important questions on Permutation and combination by Anil Verma,Director GIITJEE Chandigarh ( SCO 382,Sec 37 D,Above HDFC Bank,Chandigarh Tel : 01724652111 )
1. Find the sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time.
2. If all the letters of the word “GIITJEE” are written in all possible orders and these words are written out as in a dictionary, then find the rank of the following word “GIITJEE”
3. A man has 8 children to taken them to a zoo. He takes three of them at a time to the zoo as often as he can without taking the same 3 children together more than once. How many times will he have to go to zoo ? How many times a particular child will go ?
4. How many five digits numbers divisible by 3 can be formed using the digits 0, 1, 2, 3, 4, 7 and 8 if each digit is to be used at most once.
5. A shop sells 6 different flavours of ice–cream. In how many ways can a customer choose 4 ice–cream cones if
(i) they are all of different flavours
(ii) they are non necessarily of different flavours
(iii) they contain only 3 different flavours
(iv) they contain only 2 or 3 different flavours ?
6. In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front and 4 at the back ? How many seating arrangements are possible if 3 girls sit together in a back row on adjacent seats ?
7. A regular polygon of 10 sides is constructed. In how many ways can 3 vertices be selected so that no two vertices are consecutive ?
8. Find the number of ways in which four S come consecutively in the word
9. There are ten points in a plane. Of these ten points four points are in a straight line and with the exception of these four points, no other three points are in the same straight line. Find
(i) the number of triangles formed
(ii) the number of straight lines formed
(iii) the number of quadrilaterals formed, by joining these ten points
10. In a plane there are 37 straight lines, of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no line passes through both points A and B, and no two are parallel. Find the number of points of intersection of the straight lines.
(iv) There are r distinct objects and n distinct boxes such that n > r. Find the number of ways of
(A) putting r objects in n boxes if each box is sufficient to contain r objects.
(B) arranging r objects in n boxes so that each box contains only one object.
(C) arranging r objects in n boxes if, a box may contain any number of objects.
11. In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front and 4 at the back ? How many seating arrangements are possible if 3 girls sit together in a back row on adjacent seats ?
12. A boat is to be manned by 9 crew with 4 on the stroke side, 4 on the row side and one to steer. There are 11 crew of which 2 can stroke only, 1 can row only while 3 can steer only. In how many ways the crew can be arranged for the boat ?
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