Choose 4 shoes from 6 pairs of shoes such that there is no matching pair of shoe
ID: 3204982 • Letter: C
Question
Choose 4 shoes from 6 pairs of shoes such that there is no matching pair of shoes. How many choices are there? Choose 5 digits from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 without replacement to form a five digit number. How many different ways to form an odd number are there? Two people X and Y play ping-pong. They continue playing until either X or Y wins four games. How many different cases are possible? Consider five people: A, B, C, D, and E. How many different ways can the five people sit in a row of five chairs at a movie theatre if A and B want to sit side by side? How many different ways can five people sit in a row of five chairs at a movie theatre if A and B refuse to sit side by side? It means that there must be at least one person between A and B.Explanation / Answer
4) a) for we can choose first shoe from 12 available, second from rest of 10 3rd from rest 8 and so on
hence number of ways =12*10*8*6*4 =23040
b)as first digit can not take 0, it has 9 options , last digit has 5 options , as it can take only odd numbers, for second digit we have 9 options , 3rd we have 8 and 4 th we have 7 options.
hence total number of outcome =9*9*8*7*5 =22680
c)let X represent win for X and Y win for Y.
for 4 games there are 2 outcomes when X or Y win all 4
for 5 games number of outcomes =2*4!/(3!*1!) =8
for 6 games number of outcomes =2*5!/(3!*2!) =20
for 7 games number of outocomes =2*(6!/(3!*3!) =40
hence total number of outcome =40+20+8+2 =70
3) a) let us consider A and B as one identity cause they sit together hence we have to arrange 4 people for which number of ways =4!
as they can switch places with each other like AB and BA,hence number of ways =2*4! =48
b) totla number of ways 5 people can be arranged =5! =120
hence number of ways they do not sit together =120 -48 =72
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