Flag Magical Mathematics[Interesting Approach]> SET Theory...
question mark

How many seven -digits telephone nunber are there that begin 347- and contain at least one 0 and at least one 1?

ANS-974

shaleen upadhyay , 11 Years ago
Grade 12
anser 2 Answers
India VK

Last Activity: 11 Years ago

Let A be event that there is no zero and B be event that there is no one.

 

We need n(A'' intersect B'') or n (A union B)''

 

Use De Moivre''s theorem.

jitender lakhanpal

Last Activity: 11 Years ago

hi shaleen,

atleat one 1 and one 0 makes 3 cases

1) one 0 and one 1

then first we will select 2 out of 4 places for 0,1 and place 8 digits in remaining 2

we get C(4,2)*8^2 and the can be arranged in 2 ways so whole expression becomes

2*C(4,2)*8^2 = 768

2)2 0''S and 2 1''s

so we have to arrange them amongst each other 4!/(2!.2!) = 6

3)2 0''s and one 1

first we select 3 places out of 4 then place 8 digits in one place and arrange 2 0''s and 1 one amongst themseleves

we get the expression as C(4,3)*(3!/2!)*8

similar will be the case when there will be 2 1''s and one 0

so 2*C(4,3)*(3!/2!)*8=192

4) 3 0''s and one 1

we just have to arrange them we can do it by 4!/(3!*1!)

and similar will be the case when there are 3 1''s and one 0

so we get final expression as 4*2=8

so when we add 768+192+6+8 = 974

We are all IITians and here to help you in your IIT JEE preparation.

Now you can win by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar : Click here to download the toolbar.. 

 

Thanks and Regards

Jitender

(askIITians expert)

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments