Question

(a) In draw poker, how many ways can you get a full house? (a five card hand with 3 of one number and 2 of another number)

(b) How many 7-digit telephone numbers exist?

(c) How many 7-digit telephone numbers exist where no number is repeated?

(d) How many 7-digit telephone numbers exist where the last 3 digits are 911?

(e) How many 7-digit telephone numbers exist for a given area code if the sequence 911 can’t occur? (e.g. 838-9115 would be an illegal number)

Answer 1

a)

Full House -    3 cards of one denomination and 2 card of a second denomination.      

           
there is 13 possible cases of one denomination                      

from each set(4 cards), 3 cards are drawn in 4C3 ways                      

second denomination means 12 possible cases will occur                      

from each set(4 cards), 2 cards are drawn in 4C2 ways

                      
total number of ways =13C1*4C3*12C1*4C2 =       3744      

.......

b)

the total no of 7 digit phone numbers

=9*10*10*10*10*10*10
=9000000

= 9 * 10⁶

^c)

^{7 digit number when no number is repeated}

^{= 9 *9*8*7*6*5*4*}

^{= 544320}

^d)

^{7 digit number when last digit are 911}

^{= 9*10*10*10*1*1*1}

^{= 9000}

please revert back for doubt