Home
Class 12
MATHS
Find number of seven-digit number in the...

Find number of seven-digit number in the form of `a b c d efg(g,f,e ,` tc. Are digits at units, tens hundreds place etc.) `where a<< b<< c<< d>>e>>f>>g dot`

A

`1980`

B

`1116`

C

`1560`

D

`1476`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` Case (i) : zero not taken.
Now we have to select seven digits from `1,2,3,4,5,6,7,8,9` so ways are `"^(9)C_(7)`
From `7` digit select the largest digits as `d` from remaining `6`, we can select three digits `a`, `b`, `c` in `.^(6)C_(3)` ways.
Hence number of such numbers are `=.(9)C_(7)*^(6)C_(3)`
Case (ii) : zero taken then
`0` must be at last place, then number of such numbers are `.^(9)C_(6)*^(5)C_(3)`
So total ways `.^(9)C_(7)*^(6)C_(3)+^(9)C_(6)*^(5)C_(3)=^(9)C_(2)*^(6)C_(3)+^(9)C_(3)*^(5)C_(3)`
`=1560`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|2 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Matching Column Type|1 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE PUBLICATION|Exercise Sovled Examples|22 Videos

Similar Questions

Explore conceptually related problems

Express the following statements as a linear equation in two variables. The sum of a two digit number and the number obtained by reversing the order of its digits is 121. If the digits in unit’s and ten’s place are ‘x’ and ‘y’ respectively.

Find the number of permutations of letters a ,b ,c ,d ,e ,f,g taken all together if neither beg nor cad pattern appear.

Find the total number of nine-digit numbers that can be formed using the digits 2, 2, 3, 3, 5, 5, 8, 8, 8 so that the odd digit occupy the even places.

The total number of six-digit natural numbers that can be made with the digits 1, 2, 3, 4, if all digits are to appear in the same number at least once is a. 1560 b. 840 c. 1080 d. 480

The number of five-digit telephone numbers having atleast one of their digits repeated is a. 90000 b. 100000 c. 30240 d. 69760

If a ,b ,c ,d ,e ,f are A.M.s between 2 and 12, then find the sum a+b+c+d+e+fdot

The number of four-digit numbers that can be made with the digits 1, 2, 3, 4, and 5 in which at least two digits are identical is a. 4^5-5! b. 505 c. 600 d. none of these

The number of nine nonzero digits such that all the digits in the first four places are less than the digit in the middle and all the digits in the last four places are greater than that in the middle is a. 2(4!) b. 3(7!)//2 c. 2(7!) d. ^4P_4xx^4P_4

If a two digit positive number is multiplied by its unit digit, then the product is 189 and if the tens digit is twice of the unit digit, then find the unit digit.

How many six-digit numbers are there in which no digit is repeated, even digits appear at even places, odd digits appear at odd places and the number is divisible by 4 ? (a) 3600 (b) 2700 (c) 2160 (d) 1440