How many natural number less than 30000 can be made from the digits 0,1,2,3,4,5,6.

Dear student

 

only 1 and 2 can be used in first olace from starting.

hence 2 * 6* 5* 4*3*2 * 1 = 1440

 

Hope it helps

note that you have NOT mentioned whether repetition of digits is allowed or not. hence the ques is incomplete. i am solving assuming repetition is allowed.

we have 5 places in 30000. 

now, for first place, we can fill it in 3 ways using either of 0, 1, 2 since it should be smaller than 30000. the remaining 4 places can be filled with any digits with no restriction.

so, number of ways to fill the places= 3*7*7*7*7= 3*7^4

however, this also includes 00000, which is not a natural number.

hence total no of ways assuming repetition is allowed= 3*7^4 – 1

 

The answer to your question will be 1440

Dont put zero in the first place , and as nothing is mentioned in the question , repetition is allowed