Question

#45points



$\textbf{\underline{\underline{QUESTION }}}$





How many numbers greater than 3000 can be formed using the digits 0 , 1 , 2 , 3 , 4 and 5 , so that each digit occur at most once in each number ?




$\textbf{\underline{\underline{OPTIONS }}}$



( a ) 1000


( b ) 300


( c ) 1200


( d ) 1380

​

Answer 1

$\textbf{\underline{\underline{QUESTION }}}$

How many numbers greater than 3000 can be formed using the digits 0 , 1 , 2 , 3 , 4 and 5 , so that each digit occur at most once in each number ?

$\textbf{\underline{\underline{OPTIONS }}}$

( a ) 1000

( b ) 300

( c ) 1200

( d ) 1380

$\textbf{\underline{\underline{Answer }}}$

The correct ans is option d .

1380 no. greater than 3000 can be formed using the digits 0 , 1 , 2 , 3 , 4 and 5 , so that each digit occur at most once in each number.

Answer 2

Answer:

Option(D)

Step-by-step explanation:

The given digits are 0,1,2,3,4,5 which are 6 in number.

As the number 3000 has 4 digits and the number greater than 3000 are to be formed by using each of the given digit by once, the numbers of only 4 digits are to be formed.

(i) 4 - digit numbers:

Thousand's place can be filled by any of the digits 3 (or) 4 (or) 5 = 3 ways.

Having done that remaining 3 places can be filled by any 3 of the remaining 5 digits in P(5,3) ways.

Numbers formed = 3 * P(5,3) = 3 * 60 = 180.

                                               (or)

Numbers greater than 3000 will have 3 (or) 4 (or) 5 in the first place i.e there are 2 ways of filling the first place. Having filled the first place. Having filled the first place say by 3 we have to choose 2 digits out of the remaining 5 and the number will be P(5,3) = 60.

Therefore total of such numbers will be 3 * 60 = 180.

(ii) 5 - digit numbers:

Given that Each digit occur at most once.

= P(6,5).

Also,

Ten thousand place can be filled by 1,2,3,4,5 except 0.

Remaining 5 places can be filled by 4 in P(5,4)

Numbers formed = P(6,5) - P(5,4)

                             = 720 - 120

                             = 600

(iii) 6 - digit numbers:

Numbers formed = P(6,6) - P(5,5)

                             = 720 - 120

                             = 600.

∴ Thus, the numbers greater than 3000 will be 180 + 600 + 600 = 1380.

Hope it helps!