class 11

Math

Algebra

Permutations and Combinations

The number of integers greater than $6,000$ that can be formed, using the digits $3,5,6,7and8,$ without repetition, is :

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Is $3!+4!=7!$ ?

Number of ways in which Rs. 18 can be distributed amongst four persons such that nobody receives less than Rs. 3 is a. $4_{2}$ b. $2_{4}$ c. $4!$ d. none of these

How many $3$-digit numbers can be formed from the digits $1,2,3,4$ and $5$ assuming that.

Number of ways in which three numbers in A.P. can be selected from $1,2,3,…,n$ is a. $(2n−1 )_{2}$ if $n$ is even b. $n4n−2 $ if $n$ is even c. $4(n−1)_{2} $ if $n$ is odd d. none of these

The number of different ways in which five "alike dashes" and "eight alike" dots can be arranged using only seven of these "dashes" and "dots" is a. $350$ b. $120$ c. $1287$ d. none of these

$A$ is a set containing $n$ elements. A subset $P_{1}$ is chosen and $A$ is reconstructed by replacing the elements of $P_{1}$. The same process is repeated for subsets $P_{1},P_{2},….,P_{m}$ with $m>1$. The number of ways of choosing $P_{1},P_{2},….,P_{m}$ so that $P_{1}∪P_{2}∪….∪P_{m}=A$ is (a)$(2_{m}−1)_{mn}$ (b)$(2_{n}−1)_{m}$ (c)$(m+n)C_{m}$ (d) none of these

The value of expression $._{47}C_{4}+j=1∑5 ._{52−j}C_{3}$ is equal to a.$._{47}C_{5}$ b. $._{52}C_{5}$ c. $._{52}C_{4}$ d. none of these

How many $6−$digit numbers can be formed from the digits $0,1,3,5,7$ and $9$ which are divisible by $10$ and no digit is repeated?