document.write( "Question 949376: Find how many different odd 4-digit numbers less than 4000 can be made from the digits
\n" ); document.write( "1, 2, 3, 4, 5, 6, 7 if no digit may be repeated.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #579623 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find how many different odd 4-digit numbers less than 4000 can be made from the digits
\n" ); document.write( "1, 2, 3, 4, 5, 6, 7 if no digit may be repeated.
\n" ); document.write( "

\r\n" );
document.write( "Always take care of the most restricted things first.  We \r\n" );
document.write( "have two restrictions.  The first digit must be from the set\r\n" );
document.write( "{1,2,3} and the last digit must be from the set {1,3,5,7}\r\n" );
document.write( "\r\n" );
document.write( "Since 1 and 3 are in both sets, we have two cases.\r\n" );
document.write( "\r\n" );
document.write( "Case 1. Numbers with the first digit 1 or 3.\r\n" );
document.write( "Case 2. Numbers with the first digit 2.\r\n" );
document.write( "\r\n" );
document.write( "Case 1.  \r\n" );
document.write( "\r\n" );
document.write( "Choose the first digit 2 ways, (as 1 or 3)\r\n" );
document.write( "Choose the fourth digit 3 ways, from either {3,5,7} or {1,5,7}\r\n" );
document.write( "Choose the second digit any of the 5 remaining letters.\r\n" );
document.write( "Choose the third digit any of the 4 remaining letters.\r\n" );
document.write( "\r\n" );
document.write( "That's  ways for Case 1.\r\n" );
document.write( "\r\n" );
document.write( "Case 2.  \r\n" );
document.write( "\r\n" );
document.write( "Choose the first digit 1 way, as 2.\r\n" );
document.write( "Choose the fourth digit 4 ways, from {1,3,5,7}\r\n" );
document.write( "Choose the second digit any of the 5 remaining letters.\r\n" );
document.write( "Choose the third digit any of the 4 remaining letters.\r\n" );
document.write( "\r\n" );
document.write( "That's  ways for Case 2. \r\n" );
document.write( "\r\n" );
document.write( "Total: 120+80 = 200.\r\n" );
document.write( "\r\n" );
document.write( "FYI, here is a computer listing of all 200 numbers,\r\n" );
document.write( "20 rows of 10 each:\r\n" );
document.write( "\r\n" );
document.write( "1235 1237 1243 1245 1247 1253 1257 1263 1265 1267\r\n" );
document.write( "1273 1275 1325 1327 1345 1347 1357 1365 1367 1375\r\n" );
document.write( "1423 1425 1427 1435 1437 1453 1457 1463 1465 1467\r\n" );
document.write( "1473 1475 1523 1527 1537 1543 1547 1563 1567 1573\r\n" );
document.write( "1623 1625 1627 1635 1637 1643 1645 1647 1653 1657\r\n" );
document.write( "1673 1675 1723 1725 1735 1743 1745 1753 1763 1765\r\n" );
document.write( "2135 2137 2143 2145 2147 2153 2157 2163 2165 2167\r\n" );
document.write( "2173 2175 2315 2317 2341 2345 2347 2351 2357 2361\r\n" );
document.write( "2365 2367 2371 2375 2413 2415 2417 2431 2435 2437\r\n" );
document.write( "2451 2453 2457 2461 2463 2465 2467 2471 2473 2475\r\n" );
document.write( "2513 2517 2531 2537 2541 2543 2547 2561 2563 2567\r\n" );
document.write( "2571 2573 2613 2615 2617 2631 2635 2637 2641 2643\r\n" );
document.write( "2645 2647 2651 2653 2657 2671 2673 2675 2713 2715\r\n" );
document.write( "2731 2735 2741 2743 2745 2751 2753 2761 2763 2765\r\n" );
document.write( "3125 3127 3145 3147 3157 3165 3167 3175 3215 3217\r\n" );
document.write( "3241 3245 3247 3251 3257 3261 3265 3267 3271 3275\r\n" );
document.write( "3415 3417 3421 3425 3427 3451 3457 3461 3465 3467\r\n" );
document.write( "3471 3475 3517 3521 3527 3541 3547 3561 3567 3571\r\n" );
document.write( "3615 3617 3621 3625 3627 3641 3645 3647 3651 3657\r\n" );
document.write( "3671 3675 3715 3721 3725 3741 3745 3751 3761 3765\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "  \r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );