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InterviewSolution
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Find the number of ways in which 4 cards can be selected from a pack of 52 cards. In how many ways (i) all 4 cards are from one suit? (ii) all 4 cards are from different suits? (iii) all 4 cards are face cards? (iv) two cards are red and 2 cards are black? (v) all 4 cards are of same colour? |
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Answer» Solution :No. of ways of selecting 4 cards from 52 cards `= .^(52)C_(4)` `= (52 xx 51 xx 50 xx 49)/(1 xx 2xx 3 xx 4)` `= 270725` (i) No opf ways of selecting 4 cards of diamond from 14 cards `= .^(13)C_(4)`. No of ways of selecting 4 cards of club from 13 cards `= .^(13)C_(4)` No of ways of selecting 4 cards of hearts from 14 cards `= .^(13)C_(4)` No of ways of selecting 4 cards of spade from 13 cards `= .^(3)C_(4)` Now from ADDITION principle Required ways `=.^(13)C_(4) +^(13)C_(4) +^(13)C_(4) +^(13)C_(4)` `= 4 xx .^(13)C_(4)` `- 4xx (13 xx 12 xx 11 xx 10)/(1 xx 2 xx 3 xx 4)` `= 2860`. (ii) No. of ways of selecting one cardfrom 13 cards of diamond `= .^(13)C_(1) = 13` No. of ways of selecting one card from 13 cards of clud `= .^(13)C_(1) = 13` No of ways of selecting one card from 13 cards of spade `= .^(13)C_(1) = 13` No of ways of selecting one card from 13 cards of heart `= .^(13)C_(1) = 13` Now from multiplication principle Required ways `= 13 xx 13 xx 13 xx 13` `= 28561` (iii) No of face cards in 52 cards = 12 No of ways of selecting 4 cards from 12 cards `= .^(12)C_(4)` `= (12 xx 11 xx 10 xx 9)/(1 xx 2 xx 3 xx 4)` `= 495`. (iv) No. of ways of selecting 2 cards from 26 RED cards `= .^(26)C_(2)` No of ways of selecting 2 cards from 26 black cards `=.^(26)C_(2)` Now from multiplicarion principle Required ways `= .^(26)C_(2) xx .^(26)C_(2)` `= (26 xx 25)/(1 xx 2)xx (20 xx 25)/(1 xx 2)` `= 105625`. (v) No of ways of selecting4 cards from 26 red `=.^(26)C_(4)` Now from addition principle Required ways ` .^(26)C_(4) +^(26)C_(4)` `= 2 xx^(26)C_(4)` `= 2xx (26 xx 25 xx 24 xx 23)` `(1 xx 2xx 3 xx 4)` `= 29900`. |
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