You are tasked with designing a secure 13-digit code for the vault using the digits 0, 1,1, 2, 2, 3, 4, 4, 5, 5, 5, 6, 9. There are specific restrictions for creating the code: 1. The number must be even. 2. The hundreds digit (3rd digit from the right) must be even. Task: How many distinct 13-digit codes can be formed under these conditions? How many 7-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 7, 2, 3, 5, 5, 9.? to be less than 3 000 000 the first digit must be 1 or 2 to be an even number the last digit must be 2 or 6 2 3 5 56 - 5 4 3 2 - S 1x5 x 4x 3x2x1_ OR 2 21 W 2 1 1 1 x 5 x 4 x 3 x 2x1 _ 5 OR 2 ! * 21 6 2 1 x 2! 2 1x 2.! 5 4 2 2 2 S 1 x 5x 4x 3x 2X1 5 J R 21 5 21 21 4 I W 2 1 - - 1 x 5x 4x 3 x 2x1 5 2 21 6 2 1 . N Total = + 5 ? 51 N 21 x 21 + 2