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### Probability - Leap Year

You must have come across questions based on leap year in probability. A common mistake is to treat year 1900 as a leap year as the number 1900 is divisible by 4. However, year 1900 was not a leap year. The same holds good for years 1700, 1800 etc. You may check this by using the calendar available at your computer. The reason for this is that the Earth does not take exactly 365 days to complete a revolution around the Sun. To check a leap year among the centuries, check divisibility by 400. 1600 is divisible by 400 and hence is a leap year.

Historical Note: Julius Caesar had started the system of leap year. There used to be 1 leap year in every 4 years in his system. However, this still could not eradicate an error of 3 minutes per year. The Gregorian calendar corrected this by dropping leap year at the centuries not divisible by 400.

### Sum of the coefficients in the expansion of $(x+y)^n$ ....

If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$