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The value of sum(0leiltjle5) sum(""^(5)C...

The value of `sum_(0leiltjle5) sum(""^(5)C_(j))(""^(j)C_(i))` is equal to `"_____"`

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The correct Answer is:
211
`underset(0leiltjle5)(sumsum)(.^(5)C_(j))(.^(j)C_(i))`
`=.^(5)C_(1)..^(1)C_(0)+.^(5)C_(2)(.^(2)C_(0)+.^(2)C_(1))+"......"+.^(5)C_(5)(.^(5)C_(0)+.^(5)C_(1)+"...."+.^(5)C_(5))`
`= .^(5)C_(1)(2^(1)-1)+.^(5)C_(2)(2^(2)-1)+"....."+.^(5)C_(5)(2^(5)-1)`
`= (.^(5)C_(1).2^(1)+.^(5)C_(2).2^(2)+".....".+.^(5)C_(5).2^(5))-(.^(5)C_(1)+.^(5)C_(2)+"...."+.^(5)C_(5))`
`= [(1+2)^(5)-1][2^(5)-1]`
`= 3^(5)-2^(5)`
`= 243-32=211`
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CENGAGE-BINOMIAL THEOREM-Exercise (Numerical)
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