how many ways are there to choose four cards of different suits and different values from a deck of 52 cards.

• There are 4 suits having 13 cards each.
  So to choose different value card from each suit, we have 13 option for first suit (say diamond), then we will have 12 option for next suit (say heart), then we will have 11 option for next suit (say club) and lastly we have only 10 option for last suit (say spade)
  so total no of ways = 13c1 x 12c1 x 11c1 x 10c1 = 17160 ways.
• 9 years agoHelpfull: Yes(36) No(3)
• 13c1 x 12c1 x 11c1 x 10c1=17860 ways
• 9 years agoHelpfull: Yes(3) No(2)
• 13c1*12c1*11c1*10c1=17160
• 9 years agoHelpfull: Yes(3) No(0)
• Each suit has 13 cards.So to choose 4 cards of different suits we have 13C1 ways each.Total number of ways is 13C1*13C1*13C1*13C1 ways.
• 8 years agoHelpfull: Yes(3) No(3)
• from 52 cards select one=52c1
  after eliminating one suit and one value i.e 13+3=16, we get 36.
  again eliminate one value and suit card from this 36 cards i.e 12 each in 3 suit, we get 22.
  similarly again eliminating we get 10.
  so total is=52c1*36c1*22c1*10c1=411840
• 9 years agoHelpfull: Yes(1) No(5)
• @siddharth prakash...... i think the answer that you took out should be divisible by 4! ..... as one by one selection leads to arrangement.....pls reply
• 8 years agoHelpfull: Yes(1) No(0)
• 13C1*12c1*11c1*10c1
• 9 years agoHelpfull: Yes(0) No(0)
• ans shold be as......> (4c1*13c1)*(3c1*12c1)*(2c1*11c1)*(1c1*10c1)=411840
• 8 years agoHelpfull: Yes(0) No(0)
• 10*11*12*13=17160
• 8 years agoHelpfull: Yes(0) No(0)
• Selecting 1st card=13C1
  Selecting 2nd card=12C1
  Selecting 3rd card=11C1
  Selecting 4th card=10C1
  so multiply and get the answer
• 8 years agoHelpfull: Yes(0) No(0)
• different suits means we have 13 cards of each suite
  now,we have 13 option 2 choose 1st card
  12 for 2nd card
  11 for 3rd card
  10 for 4th card
  thus,13*12*11*10
• 8 years agoHelpfull: Yes(0) No(0)