Home
Class 12
MATHS
Given are six 0's, five 1's and four 2'...

Given are six `0'`s, five `1'`s and four `2's` . Consider all possible permutations of all these numbers. [A permutations can have its leading digit `0`].
How many permutations have the first `0` preceding the first `1` ?
(a) `"^(15)C_(4)xx^(10)C_(5)` (b) `"^(15)C_(5)xx^(10)C_(4)` (c) `"^(15)C_(6)xx^(10)C_(5)` (d) `"^(15)C_(5)xx^(10)C_(5)`

A

`"^(15)C_(4)xx^(10)C_(5)`

B

`"^(15)C_(5)xx^(10)C_(4)`

C

`"^(15)C_(6)xx^(10)C_(5)`

D

`"^(15)C_(5)xx^(10)C_(5)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` The no. of ways of arranging `2'` is `.^(15)C_(4)`.
Fill the first empty position left after arranging the `2's` with a `0`(`1` way) an pick the remaining five places from the position of reamining five zeros `.^(10)C_(5)` ways.
`:. ^(15)C_(4)xx1xx^(10)C_(5)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|2 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Matching Column Type|1 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE PUBLICATION|Exercise Sovled Examples|22 Videos

Similar Questions

Explore conceptually related problems

Given are six 0' s, five 1' s and four 2's . Consider all possible permutations of all these numbers. [A permutations can have its leading digit 0 ]. In how many permutations does the first 0 precede the first 1 and the first 1 precede first 2 .

""^(15)C_(3) + ""^(15)C_(5) + ……… +""^(15)C_(15) =

Find the value of .^(20)C_(0) xx .^(13)C_(10) - .^(20)C_(1) xx .^(12)C_(9) + .^(20)C_(2) xx .^(11)C_(8) - "……" + .^(20)C_(10) .

(1)/(1xx2)""^(25)C_(0)+(1)/(2xx3)""^(25)C_(1)+(1)/(3xx4)""^(25)C_(2)+…+(1)/(26xx27)""^(25)C_(25) is -

Find the sum of the series .^(84)C_(4)+6xx.^(84)C_(5)+15xx.^(84)C_(6)+20xx.^(84)C_(7)+15xx.^(84)C_(8) +6xx.^(84)C_(9)+.^(84)C_(10) .

Find the value of (.^(10)C_(10))+(.^(10)C_(0)+.^(10)C_(1))+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2))+"...."+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2)+"....." + .^(10)C_(9)) .

How many neutrons are present in 5xx10^(-4) moles of ""_(6)^(14)C ?

Prove that .^(n)C_(0) +5 xx .^(n)C_(1) + 9 xx .^(n)C_(2) + "…." + (4n+1) xx .^(n)C_(n) = (2n+1) 2^(n) .

How many neutrons are present in 5 xx 10^-1 moles of ^14_6C?

How many neutrons are present in 5 xx 10^-1 moles of C_6 ^14 ?

Home
Profile