IIT JEE , AIEEE Forum - Mathematics , Algebra

wnnaiit

there r 2 w balls,3 b balls, 4R balls.In how many ways 3 balls can be selected s.t. atleast 1 b ball is there given that balls of same colors are distinct

ans is 64 i know how but what is wrong with my soln

³C₁* ⁸C₂( first selecting one black ball & then out of remaining 8 selecting 2 balls)

pls dont give a soln but tell mistake in my soln because we get 84 by calc this way

saurabh_reincarnated

the method is correct.

ans. given may be wrong

***********************my fault

this is wrong

nadeemoidu

ur logic is to choose any 1 b ball and then 2 balls from 8 balls.

but u r including many cases repeatedly.

e.g.
Let the b balls be b1, b2, b3.

suppose u r choosing both b1 and b2. then it will fall under 2 categories: either u choose b1 and 2 other balls or u choose b2 and 2 other balls . so like this u get a lot of extra cases .

coolkrazy007

NO UR METHOD IS WRONG.................

case 1)select 1 b ball frm 3 nd other 2 from othrs=3c1*6c2=45

case 2)select 2 b balls nd 1 frm othrs=3c2*6c1=18

case 3)select 3 b balls nd 0 frm othrs=3c3*6c0=1

therfore 45+18+1=64

plzz rate if u like nd share wat all u know........

joyfrancis

Number of ways of selecting 3 balls such that none of them is B = 6C3 = 20

Number of ways of selecting 3 balls from all the 2 w balls,3 b balls, 4R balls = 9C3 = 84

Hence total ways of selecting three balls such that alteast one of them is B = 84-24=64 ways...(ans)

joyfrancis

@wnnaiit
By doing 3C1*8C2 you are calculating the number of of selecting 3 balls out of which EXACTLY one in B. But ATLEAST one is asked not EXACTLY one.

iitjee08aspirant

atleast 1 means 1 black 2 black or 3 black balls .............
hope u get it

wnnaiit

joyfrancis 8C2 includes all the cases i.e. ib,2b,3b

and nadeemoidu are not the cases mentioned by you desirable because all the balls of same colour are distinct

nadeemoidu

yes they r desirable. but u are counting it twice. once when u count b1 and the second time u count b2. u need to count them but only once.

wnnaiit

nadeemoidu see ur nudgebook

saurabh_reincarnated

srry to misguide u

i was in a hurry . made a blunder

SORRRRRRRRRRy

see yes ur r including many other cases

repeated same black pick ups understood

simply do this......

total no. of ways of picking - no. of pick ups wid no black balls

now dis i am 100% sure........... again sorry for prev. blunder

kane

your solution is wrong.nadeemoidu has given a perfect explanation.vaise bhi to avoid such mistakes prefer doing such questions the easy wayi.e. total possibilities-the case in which no black ball is selected simple.

do rate me if useful or nudge if any doubt.

Ask & Discuss Questions with Community & Experts