Permutations And Combinations

Question
CBSEENMA11015633

The value  of straight C presuperscript 50 subscript 4 space plus sum from straight r space equals 1 to 6 of straight C presuperscript 56 minus straight r end presuperscript subscript 3 space is

  • straight C presuperscript 55 subscript 4
  • straight C presuperscript 55 subscript 3
  • straight C presuperscript 56 subscript 3
  • straight C presuperscript 56 subscript 4

Solution

D.

straight C presuperscript 56 subscript 4 straight C presuperscript 50 subscript 4 space plus sum from straight r equals space 1 to 6 of space to the power of 56 minus straight r end exponent straight C subscript 3
rightwards double arrow to the power of 50 straight C subscript 4 space plus left square bracket to the power of 55 straight C subscript 3 space plus to the power of 54 straight C subscript 3 plus to the power of 53 straight C subscript 3 plus to the power of 52 straight C subscript 3 plus to the power of 50 straight C subscript 3 right square bracket
space equals left parenthesis to the power of 50 straight C subscript 4 space plus to the power of 50 straight C subscript 3 right parenthesis space plus space to the power of 51 straight C subscript 3 plus to the power of 52 straight C subscript 3 plus to the power of 53 straight C subscript 3 plus to the power of 54 straight C subscript 3 plus to the power of 55 straight C subscript 3
rightwards double arrow left parenthesis to the power of 51 straight C subscript 4 plus space to the power of 51 straight C subscript 3 right parenthesis plus space to the power of 52 straight C subscript 3 space plus to the power of 53 straight C subscript 3 space plus space to the power of 54 straight C subscript 3 space plus space to the power of 55 straight C subscript 3
rightwards double arrow space to the power of 55 straight C subscript 4 space plus space to the power of 55 straight C subscript 3 space equals space to the power of 56 straight C subscript 4

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