True or false: The product of any r con...

True or false: The product of any `r` consecutive natural numbers is always divisible by `r!`

Text Solution

AI Generated Solution

Topper's Solved these Questions

LOGARITHM
CENGAGE ENGLISH|Exercise All Questions|173 Videos
PROBABILITY
CENGAGE ENGLISH|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

The product of n consecutive natural numbers is always divisible by

The product of any three consecutive natural numbers is divisible by 6 (True/false).

Show that product of any n consecutive integers is always divisible by n!

Statement-1: n(n+1)(n+2) is always divisible by 6 for all n in N . Statement-2: The product of any two consecutive natural number is divisible by 2.

The sum of the cubes of three consecutive natural numbers is divisible by

Prove that the sum of two consecutive odd numbers is always divisible by four.

Property:Product of r consecutive number is divisible by r!

Find two consecutive natural numbers whose product is 20.

The product of the predecessor and successor of an odd natural number is always divisible by 2 (b) 4 (c) 6 (d) 8

CENGAGE ENGLISH-PERMUTATIONS AND COMBINATIONS-All Questions

(i) In how many ways can a pack of 52 cards be divided equally amon...
Text Solution
|
Let f(n)=sum(r=0)^nsum(k=r)^n(k r)dot Find the total number of divis...
Text Solution
|
True or false: The product of any r consecutive natural numbers is al...
Text Solution
|
Statement 1: Number of zeros at the end of 50! is equal to 12. Stateme...
Text Solution
|
Using permutation or otherwise, prove that (n^2)!/(n!)^n is an integer...
Text Solution
|
A number of 18 guests have to be seated, half on each side of a lon...
Text Solution
|
Ten persons numbered 1, 2,.....,10 play a chess tournament, each playe...
Text Solution
|
A box contains 2 white balls, 3 black balls & 4 red balls. In how many...
Text Solution
|
A man has three friends. The number of ways he can invite one frien...
Text Solution
|
A forecast is to be made of the results of five cricket matches, eac...
Text Solution
|
Number of points of intersection of n straight lines if n satisfies ...
Text Solution
|
Number of shortest ways in which we can reach from the point (0, 0, 0)...
Text Solution
|
Let f(n) be the number of regions in which n coplanar circles can...
Text Solution
|
If p, q, r are any real numbers, then (A) max (p, q) lt max (p, q, r)...
Text Solution
|
Number of ways of selecting three integers from {1,2,3, , n} if their ...
Text Solution
|
The number of ways of choosing triplet (x , y ,z) such that zgtmax{x,...
Text Solution
|
Find the value of 4C1 - 2C2
Text Solution
|
If a seven-digit number made up of all distinct digits 8, 7, 6, 4, ...
Text Solution
|
If n is number of necklaces which can be formed using 17 identical pea...
Text Solution
|
In how many ways can two distinct subsets of the set A of k(kgeq2) ...
Text Solution
|