हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा ११

Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many distinct 6-digit numbers are there?

Advertisements
Advertisements

प्रश्न

Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many distinct 6-digit numbers are there?

योग
Advertisements

उत्तर

Given numbers are 1, 1, 2, 3, 3, 4

Here 1 occurs twice, 3 occurs twice.

∴ Number of distinct 6-digit numbers

= `(6!)/(2! xx 2!)`

= `(6 xx 5 xx 4 xx 3 xx 2!)/(2! xx 2 xx 1)`

=6 × 5 × 2 × 3

= 30 × 6

= 180

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Combinatorics and Mathematical Induction - Exercise 4.2 [पृष्ठ १७८]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 4 Combinatorics and Mathematical Induction
Exercise 4.2 | Q 15. (i) | पृष्ठ १७८

संबंधित प्रश्न

In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.


How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?


If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is


The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is


English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?


If nP4 = 12(nP2), find n.


Find the rank of the word ‘CHAT’ in the dictionary.


The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:


If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r


8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?


Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are even?


Choose the correct alternative:
The product of r consecutive positive integers is divisible b


Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is


In how many ways can 5 children be arranged in a line such that two particular children of them are always together 


In how many ways can 5 children be arranged in a line such that two particular children of them are never together.


Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.


8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×