ASAP: Consider the word pROPOSITION. How many five letter words can be formed if two letters are alike and three letters are different? Consider the cases.

The letters M, N, A , E appear twice and G, T appear once.

So, the first case was where all the letters were different, thus, the number of words formed were:

6C5 . 5!(further permutation) = 720

the second case was where there were two groups of two alike letters and one different letter. Thus, the number of words formed were:

2C1 . 4C2 . 3! = 72

the third case was where there were one group of two alike letters and three different letters.

Thus, the number of words formed were:

4C1 . 5C3 . 4!= 960

thus, the total number of words were:

720 + 72 + 960 = 1752

but this answer is wrong as the Real answer is 1824.

Step-by-step explanation:

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d