How many 3 digits numbers can be formed from the digits 1,2,3,4,5 and 6 if repetition of the digit is allowed and if repetition of the digit is not allowed?

Share

The first digit can be selected in six ways; and another digit can also be selected in six ways

Including the third digit increases the number of ways to

36 \times 6=  216.

Note: If repetition is not allowed, the number of ways will be

 6 \times 5 \times 4 = 120

Q- How many 5 digits numbers can be formed from 1, 2, 3, 4, 5 if repetition of the digit is not allowed

Total Number of 5 digits Numbers which can be formed by numbers 1,2,3,4,5 (without repeating digits)

= 5\times4\times3\times2 = 5! = 120.

Q- How many numbers can be formed from 1, 2, 3, 4, 5 if repetition of the digit is not allowed

Single digit5= \;5\;ways
Two digit5\times4=\;20\; ways
three digit5\times4\times 3= \;60\; ways
four digit5\times4\times 3\times2 =\;120\; ways
five digits5\times4\times 3\times2\times1= \;120\; ways

the number of total numbers = 5 + 20 + 60 + 120 + 120=325

How many 5 digit numbers can be formed using (0-9) 0,1,2,3,4,5,6,7,8,9

10\times10\times10\times10\times10=10^5=100000

The number of signals that can be sent by 5 flags of different colors taking one or more at a time is

Solution
Number of signals using one flag

{\color{Blue} ^{5}\textrm{P}_1}= 5

Number of signals using two flags

{\color{Blue} ^{5}\textrm{P}_2} = 20

Number of signals using three flags

{\color{Blue} ^{5}\textrm{P}_3} = 60

Number of signals using four flags

{\color{Blue} ^{5}\textrm{P}_4} = 120

Number of signals using five flags

{\color{Blue} ^{5}\textrm{P}_5} = 120

Therefore, the total number of signals using one or more flags at a time is

5 + 20 + 60 + 120 + 120= 325

Q-How many four-digit numbers can be formed from the digits 1, 3, 4, 5, 6 and 7, if repetition of the digit is not allowed?… and if the numbers are greater than 5,000?

Solution

We have 6 digits available.
There are 3 ways to fill the first digit (5,6,7)
5 ways to fill the second digit
4 ways to fill the third digit
3 ways to fill the fourth digit

3×5×4×3=180

180, four-digit numbers if the numbers are greater than 5,000 can be formed from the digits 1, 3, 4, 5, 6 and 7 where the digits are used repetition is not allowed


Share
Related  Test the convergence of the series 1/3.7+1/4.9+1/5.11+... | Investigate convergence of the series 1/3.7+1/4.9+1/5.11+... | infinite series problems with solution solved problems in calculus

Leave a Reply

Your email address will not be published. Required fields are marked *

Top 5 Most Expensive Domains Ever Sold 4 Must-Try ChatGPT Alternatives: Perplexity AI, BardAI, Pi, and More! Types of Trading Techniques in the Stock Market. ChatGPT app now available in India this AI chatbot can help you make your life more productive. What is wrong with following function code?