In 22-23, answers may be left in notation form. The diamondsuit of a standard de
ID: 3094948 • Letter: I
Question
In 22-23, answers may be left in notation form. The diamondsuit of a standard deck of cards is removed from the deck,shuffled, and laid out in a row. How many arrangements are possibleso that the: 22) first and last cards are not pictures 23) middle card is a picture and the first and last cards arenot pictures ***PLEASEEE HELPPP!! WILL RATEEE ASAPPP!!!!!*** In 22-23, answers may be left in notation form. The diamondsuit of a standard deck of cards is removed from the deck,shuffled, and laid out in a row. How many arrangements are possibleso that the: 22) first and last cards are not pictures 23) middle card is a picture and the first and last cards arenot pictures ***PLEASEEE HELPPP!! WILL RATEEE ASAPPP!!!!!***Explanation / Answer
13 diamonds cards are taken out of the 52 cards. A2345678910 J QK Here, JQK are pictures This means that the first position can 10 different cards, so thelast position can have only 9 different cards: 10 * ........... *9 There are 11 cards left for the other 11 positions. This gives 11!(11*10*9*8*7*6*5*4*3*2*1) possibilities. So the number of possibilities are: 10*11!*9= 3592512000 10* ........*9 *...........*8. There are 10 cards left for the other 10 positions, which gives 10!possibilities: So the number of possibilities are: 10*10!*9*8 = 261736000 Note that if there are no restrictions, the number of possibilitiesare 13!=6227020800 Good Luck!