Mathematics, 14.09.2019 05:30 chancler

Using the digits 1 through 9, find the number of different 4-digit numbers such that: (a) digits can be used more than once.
(b) digits cannot be repeated. 2 .
(c) digits cannot be repeated and must be written in increasing order.

Answers: 3

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Answer from: patriciamelton57

a) 6561

b) 3024

c) 1296

Step-by-step explanation:

Given : Using the digits 1 through 9.

To find : The number of different 4-digit numbers such that :

(a) Digits can be used more than once.

(b) Digits cannot be repeated. 2 .

Solution :

Digits are 1,2,3,4,5,6,7,8,9

We have to form different 4-digit number let it be _ _ _ _

(a) Digits can be used more than once.

For first place there are 9 possibilities.

For second place there are 9 possibility as number repeats.

Same for third and fourth we have 9 possibility.

The number of ways are $9\times 9\times 9\times 9=6561$

(b) Digits cannot be repeated.

For first place there are 9 possibilities.

For second place there are 8 possibility as number do not repeats.

For third place there are 7 possibility as number do not repeats.

For fourth place there are 6 possibility as number do not repeats.

The number of ways are $9\times 8\times 7\times 6=3024$

c) Digits cannot be repeated and must be written in increasing order.

The number which we can use on first position are 1,2,3,4,5,6 i.e. 6

The number which we can use on second position are 2,3,4,5,6,7 i.e. 6

The number which we can use on third position are 3,4,5,6,7,8 i.e. 6

The number which we can use on fourth position are 4,5,6,7,8,9 i.e. 6

Total number of ways are $6\times 6\times 6\times 6=1296$

Answer from: Quest

the infinity sign

step-by-step explanation:

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

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Using the digits 1 through 9, find the number of different 4-digit numbers such that: (a) digits ca...