IIT JEE , AIEEE Forum - Mathematics , Algebra

nitish0991

Permutation and Combination

nitish0991

1.There are n different books and p copies of each in a library.The number of ways in which one or more than one book be selected is ? ?2.In how many ways can the word 'arrange' be arranged such that neither 2 'r' nor 2'a' are allowed to come together ?

nitish0991

pls help experts n everyone else..

nitish0991

pls help experts n everyone else..

truly

answering second question,,,u can take clue for the 1st one from this one....

In how many ways can the word 'arrange' be arranged such that neither 2 'r' nor 2'a' are allowed to come together ?

total number of letters= 7

total ways of arranging "arrange" = 7! / 2!*2! = 1260

now take 2 "r" and 2 "a" in one packet each...then total ways of arranging these 2 packets and the remaining 3 letters = 5! = 120

now ways in which 2 "r" and 2 "a" do not come together = 1260 - 120 = 1140

nadeemoidu

neither 2 'r's nor 2 'a' s can come together , so the answer given by truly is not exactly right.

we should subtract the cases in which either 2 'r's come together or 2 'a' s come together and then add the cases in which both 2 'r's and 2 'a's come together ( because it has been subtracted twice)

so the answer will be (7! / 2! x 2! ) - 2 x ( 6! / 2! ) + 5! = 1260 - 720 + 120 = 660

nitish0991

i dint understand why did u add 5! At the end ?

nadeemoidu

The cases containing both 2 'a's and 2'r's together have been subtracted twice (in the case of 'a' and 'r') . So it should be added again.

nitish0991

The logic should be this that since 2r and 2a can come together therefore v have added 5! And subtracted when either 2a or 2r come together..and not wat ur reason is:that v've added twice..Thanx anyways cuz it helped a lot..

MUDIT

WHAT I THINK IS THAT TRULY IS ABSOLUTELY CORRECT COS IF YOU READ THE QUESTION CAREFULLY IT HAS BEEN SPECIFIED THAT NIETHER 2r NOR 2a COME TOGETHER MEANS THAT BOTH THESE THINGS SHOULD HAPPEN SIMULTANEOUSLY
I THINK THERE IS A HUGE DIFFERENCE BETWEEN EITHER 2r OR 2a AND NIETHRE 2r NOR 2a

thedumbheadwithnobrain

To select more than one book

[(B₁B₁......(P+1)TIMES).......N TIMES] -1

-1 FOR SELECTION OF NO BOOK

HENCE ANSWER IS (P+1)ⁿ -1

Ask & Discuss Questions with Community & Experts