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Question
If α= mC2, then find the value of αC2.
If α= mC2, then find the value of αC2.
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Solution
We have α= mC2=m(m−1)2
(∵ nCr=n!r!(n−r)!)
Now αC2=α(α−1)2
=(m(m−1)2)(m(m−1)2−1)2=m(m−1)(m2−m−2)2×2×2=m(m−1)(m+1)(m−2)8=m(m−1)(m+1)(m−2)4×2
Multiplying with 3, numerator and denominator to make 4
Or =m(m+1)m(m−1)(m−2)4.3.2.1
=3(m+1)m(m−1)(m−2)4!
=3.m+1C4(∵nCr=n!r!(n−r)!)
We have α= mC2=m(m−1)2
(∵ nCr=n!r!(n−r)!)
Now αC2=α(α−1)2
=(m(m−1)2)(m(m−1)2−1)2=m(m−1)(m2−m−2)2×2×2=m(m−1)(m+1)(m−2)8=m(m−1)(m+1)(m−2)4×2
Multiplying with 3, numerator and denominator to make 4
Or =m(m+1)m(m−1)(m−2)4.3.2.1
=3(m+1)m(m−1)(m−2)4!
=3.m+1C4(∵nCr=n!r!(n−r)!)
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