QUESTION 29PolneIf the police have suspects, how many different ways can they select 5 for lineup based on height? (Type answer whole number )...

In how many ways can 5 players be assigned to the 5 positions on a basketball team, assuming that any player can play any position? In how many ways can 10 players be assigned to the 5 positions?

From 16 officers. A team of four officers has to be made. How many ways can the team be selected? So there is no specific order that we need to do? The first officer was in second. No, we can choose any of the four. So they're 16. Say four. Number of combinations to form a team. 16 factorial by a 16 minus for pictorial into for Victoria, this is a photo 16 Victoria by 12 Factorial and before victorious, this is 16 into 15 into folding in tow. Turgeon and do well with the one year divided by president to read into four into three into two into one. So this cancels. Each do was up 16 and 35 fifteen's a man's. It is getting harder into indeed possible number of teams comfortable.

So this problem is an application off permutation Rule number one. So there are seven cases in five agents in an investigative agency and how many different ways skin the cases be assigned. If each agent can only have one case, let's review the permutation. Rule number one. This says that the number of permutations off in objects taken on at the time, given that order is important, would equal to and factorial over n minus r factorial and take noted in this particular problem, order is important. For example, if we assign cases in this form Agent one agent to Agent free Agent four Agent five Let's say are assigned cases Case one case too. Case three case for case five this will be considered a different assignment of cases compared to if Agent One was the sign. Case five Agent to case four. Agent three, Case three Agent four case to an agent five case one. So order is important in this case. Now, to answer the question, there are seven cases, five agents. So the number or the permutation number of permutations of seven taken five at the time we're orders important is equal to seven factorial over seven minus five. Victoria is this seven factorial over two factorial and using a calculator. This is equal to 2520 different ways off assigning the cases.

In this problem. There are 10 questions on the set and we need a number of ways in which a candidate can choose. Six Out of 10, you have to choose six, symbolize 10 C6. There's nothing but 10 factorial by six factorial into four factorial, Which is six factorial into seven into 8 into nine and 10. Read it by six factorial into four. factorial is one into two, into three into four, this gets canceled. two Forgets come through with eight and this is three, so this is 7-3 to 10, which is 210. So there are 210 ways in which he can choose six questions out of 10. Now, if question one is made compulsory, this means six questions to be chosen, This is already questioned one. So for these five places we have nine possible Choices so out of 9-5, because question is already fixed, This is nothing but nancy face. Just nothing but nine factories by five factorial into four factorial, I'm factorial is nothing but five. Factory into six into seven into 8 and nine divided by five factors into one into two and do three into four. This gets canceled two into 36 which get canceled that this this is four ones for the user. just think about 14 into nine, which is 126. So that's it.

Okay, so we kept five spots and in each one of them we can place private. So in the 1st 1 we have five options for the 2nd 1 We have by options because there is repetition so we can select wise the same element. Now, in the third spot we have again five. The 4th 1 have four options and the fifth long. We also have five options. So in total, have five times five times, five times five times five oceans, meaning 5 to 5 that is 3124.