ON DIRECT PROBABILITIES. 33 



Permutations of two out of four, AB, BA, AC, CA, AD, 

 DA, BC, CB, BD, DB, CD, DC. 



Permutations of three out of four, ABC, ABD,BAC,BAD, 

 ACB, ACD, CAB, CAD, ADB, ADC, DAB, DAC, 

 BCA, BCD, CBA, CBD, BDA, BDC, DBA, DBC, 

 CDA, CDB, DCA, DCB, 



Permutations of four out of four (different arrangements of 

 four), ABCD, ABDC, BACD, BADC, ACBD, ACDB, 

 CABD, CADB, ADBC, ADCB, DABC, DACB, BCAD, 

 BCDA, CBAD, CBDA, BDAC, BDCA, DBAC, DBCA, 

 CDAB, CDBA, DCAB, DCBA, 



To find the number of permutations of one number 

 (m) out of another (n), begin with the whole number 

 (n) and write down as many numbers, reckoning down- 

 wards . as there are units in the number (m) which are to 

 be in each permutation : then multiply all together. 

 For instance : How many permutations are there of 4 

 out of 12. The answer is. 



12 x 11 x 10 x 9 or 11880 



The following table will furnish examples, or serve 

 for reference. 



