Number of ways of choosing -n- things taken -r- at a time is given as -Statement 1- Number of ways if Order matters - n-n-r-Statement 2- Number of ways if Order does not matter- n-n-r- r-Select the correct statement

Number of nbsp; ways of choosing 'n' things taken 'r' at a time is given as nbsp; Case 1: When order matters, Number of ways nbsp;=n!(n r)! nbsp; Case 2 ...

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Byju's Answer

Standard VIII

Mathematics

Number of Ways of Selecting "k" Things Out of "n" Things at a Time

Number of way...

Question

Number of ways of choosing $^{'} n^{'}$ things taken $^{'} r^{'}$ at a time is given as :

Statement 1: Number of ways if Order matters $= \frac{n!}{(n - r)!}$
Statement 2: Number of ways if Order does not matter $= \frac{n!}{(n - r)! \times r!}$

Select the correct statement

Statement

1

is true and statement

2

is false

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Statement

1

is false and statement

2

is true

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Both the statements are true

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Neither of the statements are true

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Solution

The correct option is C Both the statements are true
Number of ways of choosing $^{'} n^{'}$ things taken $^{'} r^{'}$ at a time is given as
Case 1: When order matters,
Number of ways $= \frac{n!}{(n - r)!}$
Case 2: When order does not matter
Number of ways $= \frac{n!}{(n - r)! \times r!}$

Suggest Corrections

Similar questions

Q. Number of ways of selecting

^{'} n^{'}

objects taken

^{'} r^{'}

at a time is given as

^{n} C_{r} = \frac{n!}{(n - 1)!}

, where order does not matter.

Q. Number of ways of selecting

r

things from

n

identical things is

Q. Observe the following Lists

List I	List II
A. The number of ways of answering one or more of $n$ questions	i. $\frac{^{n} P_{r}}{2 r}$
B. The number of ways of answering one or more of $n$ questions is when each question has an alternative is	ii. $2^{n} - 1$
C. The number of circular permutations of $n$ different things taken $r$ at a time is	iii. $\frac{^{n} P_{r}}{r}$
D. The number of circular permutations of $n$ things taken $r$ at a time none direction is	iv. $3^{n} - 1$
	v. $2^{n}$

Q. Assertion :A bag contains 10 balls in which 3 are identical, then number of ways of selecting 6 balls from the bag is

^{8} C_{2} +^{8} C_{4}

Reason: If a lot has n things out of which p are identical then number of ways of selecting r things from the lot is

r \sum r = r - p

^{n - p} C_{r}

r > p .

Q. Which of the following is correct number of ways for selecting

n

different things taken

k

at a time?

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Number of ways of choosing ′n′ things taken ′r′ at a time is given as : Statement 1: Number of ways if Order matters =n!(n−r)! Statement 2: Number of ways if Order does not matter=n!(n−r)!×r! Select the correct statement

The correct option is C Both the statements are trueNumber of ways of choosing ′n′ things taken ′r′ at a time is given as Case 1: When order matters, Number of ways =n!(n−r)! Case 2: When order does not matter Number of ways =n!(n−r)!×r!

Number of ways of choosing $^{'} n^{'}$ things taken $^{'} r^{'}$ at a time is given as :

Statement 1: Number of ways if Order matters $= \frac{n!}{(n - r)!}$
Statement 2: Number of ways if Order does not matter $= \frac{n!}{(n - r)! \times r!}$

Select the correct statement

The correct option is C Both the statements are true
Number of ways of choosing $^{'} n^{'}$ things taken $^{'} r^{'}$ at a time is given as
Case 1: When order matters,
Number of ways $= \frac{n!}{(n - r)!}$
Case 2: When order does not matter
Number of ways $= \frac{n!}{(n - r)! \times r!}$