Maharashtra State BoardHSC Commerce 11th
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Find r if 11C4+11C5+12C6+13C7=14Cr - Mathematics and Statistics

Sum

Find r if `""^11"C"_4 + ""^11"C"_5 + ""^12"C"_6 + ""^13"C"_7 = ""^14"C"_"r"`

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Solution

Use `""^"n""C"_"r" + ""^"n""C"_("r" - 1) = ""^("n" + 1)"C"_"r"`

∴ `""^11"C"_4 + ""^11"C"_5 + ""^12"C"_6 + ""^13"C"_7 = ""^14"C"_"r"`

∴ `(""^12"C"_5 + ""^12"C"_6) + ""^13"C"_7 = ""^14"C"_"r"`

∴ `(""^13"C"_6 + ""^13"C"_7) =  ""^14"C"_"r"`

∴ `""^14"C"_7 = ""^14"C"_"r"`
If nCx = nCy, then either x = y or x = n − y

∴ r = 7 or r = 14 − 7 = 7

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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.7 | Q 7 | Page 90
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