SATHEE: Permutations and Combinations 2 Question 13

Permutations and Combinations 2 Question 13

13. The value of the expression $^{47} C_{4} + \sum_{j = 1}^{5}^{52 - j} C_{3}$ is

(a) $^{47} C_{5}$

(b) $^{52} C_{5}$

(d) None of these

(1980, 2M)

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Answer:

Correct Answer: 13. (c)

Solution:

Here, $^{47} C_{4} + \sum_{j = 1}^{5}^{52 - j} C_{3}$

$=^{47} C_{4} +^{51} C_{3} +^{50} C_{3} +^{49} C_{3} +^{48} C_{3} +^{47} C_{3}$

$= (^{47} C_{4} +^{47} C_{3}) +^{48} C_{3} +^{49} C_{3} +^{50} C_{3} +^{51} C_{3}$

[using $^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r}$ ]

$= (^{48} C_{4} +^{48} C_{3}) +^{49} C_{3} +^{50} C_{3} +^{51} C_{3}$

$= (^{49} C_{4} +^{49} C_{3}) +^{50} C_{3} +^{51} C_{3}$

$= (^{50} C_{4} +^{50} C_{3}) +^{51} C_{3}$

$=^{51} C_{4} +^{51} C_{3} =^{52} C_{4}$

Permutations and Combinations 2 Question 13

13. The value of the expression $^{47} C_{4} + \sum_{j = 1}^{5}^{52 - j} C_{3}$ is

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Permutations and Combinations 2 Question 13

13. The value of the expression 47C4+∑j=1552−jC3 is

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13. The value of the expression $^{47} C_{4} + \sum_{j = 1}^{5}^{52 - j} C_{3}$ is