0
Want this question answered?
Be notified when an answer is posted
Add your answer:
Earn +20 pts
How many 3-digit numbers can be formed using the digit 123456 and 7 if no digit can be repeated in number?
With questions like these it is often difficult to remember whether we are looking for permutations or combinations. In English we use these two terms interchangeably but in mathematics we must be more precise. The way to remember is that if the order matters, then position matters, thus position = permutation. If order does not matter then we're looking for combinations. Put simply, 123 and 321 are the same combination but different permutations. In this case we're looking for permutations (thus combination locks should really be called permutation locks).The formula for calculating permutations is fairly simple: given 7 digits from which we must select 3, we have 7^3 = 7 x 7 x 7 = 343 permutations in total. However, in order to exclude repeated digits we must use a different formula. When we select the first digit we have 7 choices (just as we do with repetition allowed), but when we choose the next digit we only have 6 choices remaining and for the final digit we only have 5 choices remaining.To express this more mathematically, we need to use factorials. Factorial 7 (written 7!) is 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040. This tells us there are 5040 different ways we can write all the digits from 1 to 7 without repetition. In order to calculate all the 3-digit permutations we need to stop multiplying when we reach 4. To achieve this, we use the following formula:n! / (n-m)!where n is the number of elements in the set and m is the number of elements we wish to select.Thus we get:7! / (7-3)! = 7! / 4!If we (partially) expand this we find we have:7 x 6 x 5 x 4! / 4!The 4!s above and below the division will cancel each other out, so we get:7 x 6 x 5 = 210 permutations without repetition.If we were to fully expand this out we find we have:(7 x 6 x 5 x 4 x 3 x 2 x 1) / (4 x 3 x 2 x 1) = 5040 / 24 = 210 permutations without repetition.Note that if we were only interested in the number of combinations (without repetition), we divide the number of permutations by 3! For that we use the following formula instead:n! / (m! x (n-m)!)Thus we'd get:7! / (3! x 4!) = (7 x 6 x 5 x 4!) / (3 x 2 x 1 x 4!)The 4!s cancel each other out so we get:(7 x 6 x 5) / (3 x 2 x 1) = 210 / 6 = 35 combinations without repetition.
Print the digits in a number in ascending or descending order c program?
#include/* In case pow does not work from math.h */int my_pow( int x, int y ){int i, result = 1;for( i=1; i temp2 ){if ( 1 == j ){printf(" %d, ", i );break;}j--;}else{break;}}while(1);}printf("\n");return 1;}OUTPUT:------------[~/temp-satish]$ ./a.outEnter number of digits :212, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 56, 57, 58, 59, 67, 68, 69, 78, 79, 89,[~/temp-satish]$[~/temp-satish]$ ./a.outEnter number of digits :3123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 145, 146, 147, 148, 149, 156, 157, 158, 159, 167, 168, 169, 178, 179, 189, 234, 235, 236, 237, 238, 239, 245, 246, 247, 248, 249, 256, 257, 258, 259, 267, 268, 269, 278, 279, 289, 345, 346, 347, 348, 349, 356, 357, 358, 359, 367, 368, 369, 378, 379, 389, 456, 457, 458, 459, 467, 468, 469, 478, 479, 489, 567, 568, 569, 578, 579, 589, 678, 679, 689, 789,[~/temp-satish]$ ./a.outEnter number of digits :41234, 1235, 1236, 1237, 1238, 1239, 1245, 1246, 1247, 1248, 1249, 1256, 1257, 1258, 1259, 1267, 1268, 1269, 1278, 1279, 1289, 1345, 1346, 1347, 1348, 1349, 1356, 1357, 1358, 1359, 1367, 1368, 1369, 1378, 1379, 1389, 1456, 1457, 1458, 1459, 1467, 1468, 1469, 1478, 1479, 1489, 1567, 1568, 1569, 1578, 1579, 1589, 1678, 1679, 1689, 1789, 2345, 2346, 2347, 2348, 2349, 2356, 2357, 2358, 2359, 2367, 2368, 2369, 2378, 2379, 2389, 2456, 2457, 2458, 2459, 2467, 2468, 2469, 2478, 2479, 2489, 2567, 2568, 2569, 2578, 2579, 2589, 2678, 2679, 2689, 2789, 3456, 3457, 3458, 3459, 3467, 3468, 3469, 3478, 3479, 3489, 3567, 3568, 3569, 3578, 3579, 3589, 3678, 3679, 3689, 3789, 4567, 4568, 4569, 4578, 4579, 4589, 4678, 4679, 4689, 4789, 5678, 5679, 5689, 5789, 6789,[~/temp-satish]$
How many pages are in the book Emmy and the Home For Troubled Girls?
It has a total of 346 pages.
What is 346 of an inch?
346 of an inch is either 346 inches. or 1/346 = 0.00289 inches
What are the factors of 346?
The positive integer factors of 346 are: 1, 2, 173, 346
How many factors does 346 have?
346 has four factors: 1, 2, 173, 346.
How do you write 346 over 1000 in decimal notation?
You divide 346 by 1,000 and get .346.
What is the factor tree for 346?
346 2,173
Is 346 divisible by 2 and 3?
No. 346/2 = 173 346/3 = 1151/3
What is the product of 45 and 346?
46 x 346 = 15916
What is 950degrees Fahrenheit minus -346 degrees Fahrenheit?
950 - 346 = 604 950 - (-346) = 1296
How do you write 346 in standard notation?
346 is the standard notation. The standard form is 3.46 × 102
What equals 346?
7 times what equals 346
What is 502 times 346?
502 * 346 = 173,692
