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

Thank you for the answer. Please answer the second question also.

Thank you for your answer. Please answer the second question that i've posted.