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16 Dec 2024, 01:27
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GGGMAT2
What about other overlaps? Such as 177, 277, 377, ..., 977. Also, 707, 717, 727, 737, 747, 757, 767, 787, 797.
14 Mar 2025, 11:09
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HouseStark
COULD YOU SHARE THE FORMULA HOW DID YOU HAVE NO OF INTEGERS IN WHICH 7 DOESN'T APPEAR
15 Apr 2025, 02:56
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Set theory can also be used here =>
P(A) + P(B) + P(C) - P(A∩B) - P(A∩C) - P(B∩C) + P(A∩B∩C)
P(A) = 7 can occur in units digit in 10*10 ways = 100
P(B) = 7 can occur in tenths digit in 10*10 ways = 100
P(C) = 7 can occur in hundredths digit in 10*10 ways = 100
P(A∩B) = 7 can occur in units and tenths digit in 10 ways = 10
P(A∩C) = 7 can occur in units and hundredths digit in 10 ways = 10
P(B∩C) = 7 can occur in tenths and hundredths digit in 10 ways = 10
P(A∩B∩C) = 7 can occur in units, tenths and hundredths digit in 1 way = 1
Total = 100 + 100 + 100 - 10 - 10 - 10 + 1 = 271
IMO: E
P(A) + P(B) + P(C) - P(A∩B) - P(A∩C) - P(B∩C) + P(A∩B∩C)
P(A) = 7 can occur in units digit in 10*10 ways = 100
P(B) = 7 can occur in tenths digit in 10*10 ways = 100
P(C) = 7 can occur in hundredths digit in 10*10 ways = 100
P(A∩B) = 7 can occur in units and tenths digit in 10 ways = 10
P(A∩C) = 7 can occur in units and hundredths digit in 10 ways = 10
P(B∩C) = 7 can occur in tenths and hundredths digit in 10 ways = 10
P(A∩B∩C) = 7 can occur in units, tenths and hundredths digit in 1 way = 1
Total = 100 + 100 + 100 - 10 - 10 - 10 + 1 = 271
IMO: E
