The number of different 7 digit numbers that can be written using only the three digits 1, 2 and 3 with the condition that the digit 2 occurs twice in each number is

Other than 2, remaining five places are to be filled by by 1 and 3∴ number of ways for five places = 2 × 2 × 2 × 2 × 2 = 25For 2, selecting 2 places out of 7=7C2∴ Required no. of ways =7C2⋅25.