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How many 4-digit numbers can you build if the number must be odd odd digits can be repeated and even digits cannot be repeated?
Given (reworded a little):Length (L) = 4Must be an odd number is the same as saying it must end in an odd numberOdd digits: 1, 3, 5, 7, 9 (nodd = 5)Even digits: 0, 2, 4, 6, 8 (neven = 5)n = Odd + Even = 10Odd digits can be repetitiveEven digits cannot be repetitiveAssuming we are not counting numbers that start with a 0, because they simplify into three digit numbers. (i.e., 0123 = 123)First figure how how many four digit numbers in total you can have. This optional step gives you a check for your final answer, to make sure it makes sense.I'll use square brackets to illustrate what can be in the boxes.[n-1][10][10][10] = (9)(103) = 9000 total possibilities (this makes since because 9999 = 9000)Because our number has to be odd:[n-1][10][10][nodd] = (9)(5)(102) = 4500 total odd possibilitiesAny number over 4500 does not make since for a final answer.Break this into cases to simplify it.Case 1: Number starts with an even number (remember if it starts with an odd number, we need to exclude zero). The first term will always be neven-1, but the next term, 0 is allowed, but you still have to remove the number you just used so it will also be neven-1.EEEO => [neven-1][neven-1][neven-2][nodd] = 4 x 4 x 3 x 5 = 240EOEO =>[neven-1][nodd][neven-1][nodd] = 4 x 5 x 4 x 5 = 400EEOO =>[neven-1][neven-1][nodd][nodd] = 4 x 4 x 5 x 5 = 400EOOO =>[neven-1][nodd][nodd][nodd] = 4 x 5 x 5 x 5 = 500Case 1 total = 240 + 400 + 400 + 500 = 1540 possibilitiesCase 2: Number starts with an odd numberOOOO => [nodd][nodd][nodd][nodd] = 5 x 5 x 5 x 5 = 625OEOO =>[nodd][neven][nodd][nodd] = 5 x 5 x 5 x 5= 625OOEO =>[nodd][nodd][neven][nodd] = 5 x 5 x 5 x 5= 625OEEO =>[nodd][neven][neven-1][nodd] = 5 x 5 x 4 x 5 = 500Case 2 total = 625 + 625 + 625 + 500 = 2375 possibilitiesAdd Case 1 and Case 2 totals up:1540 + 2375 = 3915 possibilitiesCheck your answer against all odd number possibilities:3915 < 4500, therefore our answer makes sense.The answer is 3915 possibilities.To check your work, try to find how many odd numbers have even numbers that repeat and subtract that from the total odd possibilities we found first. In this case though, this check is harder than the actual problem. You have to consider the EEEO, EOEO, EEOO, and OEEO cases. However the EEEO case breaks into three further cases, depending on which E is repeating.
Where did Cain live in biblical times?
Religious scholars speculate that the Garden of Eden was near the Persian Gulf, in what is now southern Iraq. After that, Cain went east (Gen. ch.4).
Sould you kiss a guy to prove to people that you are not prude?
No you shouldn't you shouldn't have to proove anything to anyone! if they think your a prude just nodd and say okay whatever you think!
You nodd with him a lot when you see him staring at you during one class and sometimes he imitates you but he ignores you the rest of the day what is he trying to say?
hes saying get lost you ugly mole of a woman. just go die
What movie and television projects has Andy Chworowsky been in?
Andy Chworowsky has: Performed in "Tou qing ke" in 1985. Performed in "Ninja the Protector" in 1986. Performed in "Diamond Ninja Force" in 1988. Played Nodd and Druul in "Dream Defenders" in 2011. Played Andy in "Ninja the Mission Force" in 2012.
What actors and actresses appeared in Dream Defenders - 2011?
The cast of Dream Defenders - 2011 includes: Andy Chworowsky as Nodd and Druul Henry Coombs as Dr. Mercer Henry Coombs as Dreamer Catherine Fu as Hera Catherine Fu as Steph Muriel Hofmann as Zoey Matthew Leonhart as young Alec Daedelus Matthew Leonhart as Zeus
What are the 5 lands that can be found on Antarctica?
* Ellsworth Land * Marie Byrd Land * Edward VII Land * Palmer Land * Victoria Land * Oates Land * George V Land * Terre Adelie * Wilkes Land * Queen Mary Land * Wilhelm II Land * Princess Elizabeth Land * Mac RObertson Land * Kemp Land * Enderby Land * Dronning Maud Land * Coats Land
Musicians from this land is your land this land is my land?
did u mean the song this land is my land this land is your land from california to the new york island if ya did than its a random singer that makes cool songs
When was This Land Is Your Land created?
This Land Is Your Land was created in 1945.
Sentence using land to land?
Is there enough land to land the airplane safely.
The ancient Egyptians called their land the black land what else did they call their land?
they called their land the red land
A paleontologist finds a plant fossil that shows that the plant had seeds What can the paleontologist conclude?
It was a land plant.
