SATHEE: Permutations and Combinations 4 Question 7

Permutations and Combinations 4 Question 7

7. In how many ways can a pack of 52 cards be

(i) divided equally among four players in order

(ii) divided into four groups of 13 cards each

(iii) divided in 4 sets, three of them having 17 cards each and the fourth just one card?

$(1979, 3$ М)

Show Answer

Answer:

Correct Answer: 7. ((i) $\frac{(52)!}{(13!)^{4}}$ (ii) $\frac{(52)!}{4! (13!)^{4}}$ (iii) $\frac{(52)!}{3! (17)^{3}}$ )

Solution:

(i) The number of ways in which 52 cards be divided equally among four players in order

$=^{52} C_{13} \times^{39} C_{13} \times^{26} C_{13} \times^{13} C_{13} = \frac{(52)!}{(13!)^{4}}$

(ii) The number of ways in which a pack of 52 cards can be divided equally into four groups of 13 cards each $= \frac{^{52} C_{13} \times^{39} C_{13} \times^{26} C_{13} \times^{13} C_{13}}{4!} = \frac{(52)!}{4! (13!)^{4}}$

(iii) The number of ways in which a pack of 52 cards be divided into 4 sets, three of them having 17 cards each and the fourth just one card

$= \frac{^{52} C_{17} \times^{35} C_{18} \times^{18} C_{17} \times^{1} C_{1}}{3!} = \frac{(52)!}{3! (17)^{3}}$

Permutations and Combinations 4 Question 7

7. In how many ways can a pack of 52 cards be

Answer:

Solution:

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Permutations and Combinations 4 Question 7

7. In how many ways can a pack of 52 cards be

Answer:

Solution:

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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