मराठी

How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?

Advertisements
Advertisements

प्रश्न

How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?

बेरीज
Advertisements

उत्तर

Those numbers divisible by 10 are those in which 0 is placed in the ones place.

Therefore, 0 is fixed at the units place.

Therefore, there will be as many ways as there are ways of filling 5 vacant places  

in succession by the remaining 5 digits (i.e., 1, 3, 5, 7 and 9).

The 5 vacant places can be filled in 5! ways.

Hence, required number of 6-digit numbers = 5! = 120

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Permutations and Combinations - Miscellaneous Exercise [पृष्ठ १२३]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
पाठ 6 Permutations and Combinations
Miscellaneous Exercise | Q 5. | पृष्ठ १२३

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

How many chords can be drawn through 21 points on a circle?


In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?


Prove that

\[\frac{1}{9!} + \frac{1}{10!} + \frac{1}{11!} = \frac{122}{11!}\]

A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?


There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?


Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?


From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?


How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?


Evaluate the following:

12C10


If nC12 = nC5, find the value of n.


If nC4 = nC6, find 12Cn.


If 15Cr : 15Cr − 1 = 11 : 5, find r.


If 28C2r : 24C2r − 4 = 225 : 11, find r.


There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:

a particular student is excluded.


How many different selections of 4 books can be made from 10 different books, if
there is no restriction;


How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?


From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer


A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has(iii) at least 3 girls? 


We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can the selection be made?


Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.


A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: at least 3 girls?


If C (n, 12) = C (n, 8), then C (22, n) is equal to


Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3


Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120


There are 8 doctors and 4 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.


Find the value of 15C4 + 15C5 


Find the value of 20C16 – 19C16 


In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?


The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l2, k points on l3. The maximum number of triangles formed with vertices at these points are ______.


There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.


Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is ______.


The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.


There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.


If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.


Number of selections of at least one letter from the letters of MATHEMATICS, is ______.


There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.


From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×