p&c

sry.....i dont hve da answers rite now!!:p

mak do u mean to say LRFB BBBBB
& RLFB BBBBB

WILL BE COUNTED IN THE SAME CASE????

COZ DA QUE ASKS IN HOW NMANY WAYS CAN HE TAKE 9 STEPS SO I THINK THEY SHUD B DIFF YAAAARRRR!!!!!!!!!

SO DA ANS SHUD BE (9P4 * 4^5)

for 1st its 49.
for 2nd its 4*3*2*1*⁹c₄*4⁵
for third i haven't calculated but nishant bhaiya is right.
plz post the ans i will calculate the third and check my ans.

but why....???????

i dont agree unless someone points out my mistake... anywayzzz... sorry, if i'm wrong... [2]

Hey mak
In part 2 of the question

dont u thik da ans shud be 9P₄
bcoz those directions selected can be in any arrangement!!!!

from the above explanation, u may raise a doubt .... "If dat is d case, then multiplying 220 with 4! (since each case gives 4! new cases) must give d desired answer, but it doesn't. y...? "

this is not true because there are many more possibilities... not just 4! , but many moreeeee...!!!!!

[infact i got this doubt while posting d above reply, dunno whether u'll get dis doubt or not... [6] [4] ]

@shreya...

in ur method, the error is... :

u've considered all d 9 steps as identical... where as, they are all different...

more precisely... in ur equation x1 + x2 + x3 + x4 = 9... if v solve by ur method, v assume dat (0,2,3,4) and (2,3,4,0) are same... where as, here they are different solutions...

practically speaking, taking 2 steps in north direction and one step in west direction is not equal to taking one step north, one west and then one north... though both of them will land u up at d same point...

hope its clear now... [1]

Explanations for my answers...

1) As already said by nishant bhaiya, each individual step can be taken in 4 ways irrespective of d previous n further steps...

hence the total no. of ways = 4.4.4...(9 times) = 4⁹ ways...

2) Selecting four of d total nine steps in ⁹C₄ ways... and it can be assumed that each of the four steps are taken in four different directions... now the remaining 5 steps can be taken in any direction in 4⁵ ways...

hence total no. of such cases possible = ⁹C₄.4⁵ ways...

3) This one is interesting...

First step can be taken in any direction in 4 ways... now, for each step taken later on, one counter step should be taken... only then it is possible for him to be one step away from starting point... (think over this, it's d easiest way to solve dis problem...!!!) hence if v decide any of the four steps, the other four steps (since total steps remaining after first step are 8) will be counter steps to these four... [note : counter step means a step taken in d opposite direction to d step already taken... its not necessary that same step should be reversed, but it must be in d opposite direction, or rather... a counter step means an anti-parallel step]

hence, no. of ways this can be done = 4.4⁴ = 4⁵ ways...

[1]

correct me if i've gone wrong anywhere in my interpretation...

i hve done da first part... n i m nt gettin 4⁹..

my ans is 220 ways...

solved it by integral equation method
it will be x₁ + x₂ + x₃ + x₄ = 9
constraints will be 0<=x₁<=9, 0<=x₂<=9, 0<=x₃<=9, 0<=x₄<=9..

and on solving dis u get coeffiecient of x⁹ in (1-x)^-4
so ans is ¹²C₉. ie 220 ways..

i think for 2nd part also we can solve by dis method n in 3rd part we would hve to make cases...

do correct me if i m wrong....

For d first one... ans is 4⁹

For d second one... ans is ⁹C₄.4⁵

For d third one... ans is 4.(4⁴)

[1]

correct me if i'm wrong...

for the third part i am getting 16 ways

adi i am getting 6*4⁵

can we do da 3rd part lik dis..

we want steps in forward direction= dat in backward direction
n steps in left = steps in right

n then we make cases

i think ans for 2 is 40

n what abt part 3 of da ques

nishant sir i have edited dat :P