Question

Evaluate 10c1 + 10c2 +10c3 +10c4+......+ 10c10

Answer 1

Here is your answer

Have you studied Pascal's Triangle? 

It looks like this 

...........1............ This can be called the zero row and its sum is 1 

.........1...1...........this is the 1 row and its sum is 2=2¹ 

.......1..2....1...... this is the 2 row and its sum is 4 = 2² 

.....1..3..3...1....this is the 3 row and its sum is 8=2³ 

..1...4..6..4...1 this is the 4 row and its sum is 16=2^4 

so the 10C0 + 10C1+....+10C9+10C10 is the sum 

of the 10 row and it would be 2^10 = 1024 

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??????Edit for please show the working?????? 

Work is shown. We constructed Pascal's triangle and 

I showed the sum of the zero row, the sum of the 1 row. 

Hopefully you know that a sum is an answer to an addition problem. 

The SUM { what you get when you add the elements} of 

the nth row of Pascal's Triangle is 2^n , if we assume 

the first row is row zero. 

2^10 = 2 times itself 10 times. 

The only other work that could be shown is a fully 

drawn out 

10C0 + 10C1 + ... 

= 1 + 10 + 10(9)/1*2 + 10(9)(8)/1*2*3 +.....and

this is long, that is the reason for developing the formula 

Σ 10Cx = 2^(10) 

x=0 to x=10

Hope it helps

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