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