please do 1-9 1. An MP3 player has a playlist with 12 songs. You select the shuf

Question

please do 1-9

1. An MP3 player has a playlist with 12 songs. You select the shuffle option, which plays each song in a random order without repetition, for the playlist. In how many different orders can the songs be played? There are 10 runners in a race. Medals are awarded for 1st, 2nd, and 3rd place. In how many different ways can the medals be awarded? 2. There are 9 players on a baseball team. In how many different ways can the coach choose players for first base, second base, third base, and shortstop? 3. 4. A bag contains 9 tiles, each with a different number from 1 to 9. You choose a tile without looking, put it aside, choose a second tile without looking, put it aside, then choose a third tile without looking. What is the probability that you choose tiles with the numbers 1, 2, and 3 in that order? There are 11 students on a committee. To decide which 3 of these students will attend a conference, 3 names are chosen at random by pulling names one at a time from a hat. What is the probability that Sarah, Jamal, and Mai are chosen in any order? 5. 6. A clerk has 4 different letters that need to go in 4 different envelopes. The clerk places one letter in each envelope at random. What is the probability that all 4 letters are placed in the correct envelopes?

Explanation / Answer

1. There are 12 songs and they are to be shuffled in random order without repetition.

Assume you have 12 items and you have 12 spaces. You have to put these item in these places. We will go place by place.

For place 1, we have 12 options of items. This can be filled in 12 ways.

For place 2, we have 11 options (because we have already filled place 1 by one og the item and there is no repetition. So place 2 can be filled in 11 ways.

Similary, place 3 can be filled in 10 ways and so on...

Now since all the places are to be filled, its 'and' situation. So we will mutiply for getting the total possibilities

So number of total ways of shuffling=12*11*10*9*8*7*6*5*4*3*2*1 = 12! = 47,90,01,600 ways.

Note: It'd be great if you could ask all the questions seperately :)

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