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1. A 4 letter word is written down by taking letters from the word KANYAKUMARI. What is the chance of the word to be of all different letters?
2. A card is drawn from a pack of 52 cards. The card is then replaced and the pack is reshuffled. It is done 6 times. Find the chance that the cards drawn are 2 hearts, 2 diamonds & 2 blacks.
Dear Abhipsa
KANYAKUMARI =2 K +3 A + 1N + 1Y + 1U + 1M + 1R +1I
Case letter does not include A and K
total number of 4 letter word can be formed =6C4 4!................1
total number of 4 letter word that has different letter can be formed =6C4 4!................2
case letter include A but not K
total number of 4 letter word can be formed =1*6C3 4! + 1*1*6C2 4!/2! +1*1*1*6C1 4!/3! ( when 1 A ,2A and 3A are included respestively)...............3
total number of 4 letter word that has different letter can be formed =1* 6C3 4! ...........4
case letter include K but not A
total number of 4 letter word can be formed =1*6C3 4! + 1*1*6C2 4!/2! + ( when 1 K ,2K are included respestively).................5
total number of 4 letter word that has different letter can be formed =1* 6C3 4!...............6
case letter K and A both included
total number of 4 letter word can be formed =1*1*6C2 4! + 1*2*6C1 4!/2! + 1*3*6C0 4!/3! +2*1*6C2 4!/2! +2*2*6C0 4!/2! 2!( when 1 K 1A ,1K2A,1K3A,2k1A,2K 2A are included respestively).................7
total number of 4 letter word that has different letter can be formed =1*1* 6C2 4!...............8
so pobability =(2+4+6+8)/(1+3+5+7)
put value of above equation and calculate
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Thank you for your answer. Please answer the second question that i've posted.
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