Home
Class 12
MATHS
The number of ways of choosing 10 object...

The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is:

A

`2^(20)`

B

`2^(20)+1`

C

`2^(30)-1`

D

`2^(21)`

Text Solution

Verified by Experts

The correct Answer is:
A
Consider following cases 10 distinct or 9 distinct or 8 distinct … 0 distinct.
`rArr" ".^(21)C_(10)+.^(21)C_(9)+.^(21)C_(8)…………….^(21)C_(0)=s" (say)" …(i)"`
`.^(21)C_(11)+.^(21)C_(12)…^(21)C_(20)+.^(21)C_(21)s" ...(ii)" Apply ".^(n)C_(t)=.^(n)C_(n-r)`
`25=2^(21)" Adding i and ii "s=2^(20)`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST- 16

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • JEE MAIN REVISION TEST 8 (2020)

    VMC MODULES ENGLISH|Exercise MATHEMATICS ( SECTION 2 )|5 Videos

  • JEE MAIN REVISION TEST- 24

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION - 2)|5 Videos

Similar Questions

Explore conceptually related problems

Statement 1: Number of ways of selecting 10 objects from 42 objects of which 21 objects are identical and remaining objects are distinct is 2^(20)dot Statement 2: ^42 C_0+^(42)C_1+^(42)C_2++^(42)C_(21)=2^(41)dot

Statement 1: Number of ways of selecting 10 objects from 42 objects of which 21 objects are identical and remaining objects are distinct is 2^(20)dot Statement 2: ^42 C_0+^(42)C_1+^(42)C_2++^(42)C_(21)=2^(41)dot

Prove that the number of ways to select n objects from 3n objects of whilch n are identical and the rest are different is 2^(2n-1)+((2n) !)/(2(n !)^2)

Statement 1: When number of ways of arranging 21 objects of which r objects are identical of one type and remaining are identical of second type is maximum, then maximum value of ^13 C_ri s78. Statement 2: ^2n+1C_r is maximum when r=ndot

The number of ways in which five distinct objects can be put into three identical boxes so that no box remains empty is

Find the number of ways of selecting 10 balls out of an unlimited number of identical white, red, and blue balls.

If N denotes the number of ways of selecting r objects of out of n distinct objects (rgeqn) with unlimited repetition but with each object included at least once in selection, then N is equal is a. .^(r-1)C_(r-n) b. .^(r-1)C_n c. .^(r-1)C_(n-1) d. none of these

Find the number of ways of selecting 3 pairs from 8 distinct objects.

Find the number of ways of selecting 3 pairs from 8 distinct objects.

Number of ways in which 6 distinct objects can be kept into two identical boxes so that no box remains empty is