SATHEE: Permutations and Combinations 2 Question 9

Permutations and Combinations 2 Question 9

9. Let $S = 1, 2, 3, \dots \dots, 9$ . For $k = 1, 2, \dots \dots .5$ , let $N_{k}$ be the number of subsets of $S$ , each containing five elements out of which exactly $k$ are odd. Then $N_{1} + N_{2} + N_{3} + N_{4} + N_{5} =$ (2017 Adv.)

(a) 210

(b) 252

(d) 125

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Answer:

Correct Answer: 9. (c)

Solution:

$N_{i} =^{5} C_{k} \times^{4} C_{5 - k}$

$\begin{aligned} N_{1} = 5 \times 1 \\ N_{2} = 10 \times 4 \\ N_{3} = 10 \times 6 \\ N_{4} = 5 \times 4 \\ N_{5} = 1 \\ N_{1} + N_{2} + N_{3} + N_{4} + N_{5} = 126 \end{aligned}$

Permutations and Combinations 2 Question 9

9. Let $S = 1, 2, 3, \dots \dots, 9$ . For $k = 1, 2, \dots \dots .5$ , let $N_{k}$ be the number of subsets of $S$ , each containing five elements out of which exactly $k$ are odd. Then $N_{1} + N_{2} + N_{3} + N_{4} + N_{5} =$ (2017 Adv.)

Answer:

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Permutations and Combinations 2 Question 9

9. Let S=1,2,3,……,9. For k=1,2,…….5, let Nk be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N1+N2+N3+N4+N5= (2017 Adv.)

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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9. Let $S = 1, 2, 3, \dots \dots, 9$ . For $k = 1, 2, \dots \dots .5$ , let $N_{k}$ be the number of subsets of $S$ , each containing five elements out of which exactly $k$ are odd. Then $N_{1} + N_{2} + N_{3} + N_{4} + N_{5} =$ (2017 Adv.)