# Count of strings that can be formed using a, b and c under given constraints

Given a length n, count the number of strings of length n that can be made using a, b and c with at-most one b and two cs allowed

**Example:**

Input:
n=1
Output:
3
Possible strings are:
"a", "b", "c"
Input:
n=2
Output:
8
Possible strings are:
"aa", "ab", "ac", "ba", "ca", "bc", "cb", "cc"

String alphabets are only {a, b, c}

Length of string is n. (n>0)

Let's consider what can be the possible cases

'a', i.e., n'a'forms the string.Count of such string is: 1

'b'& n-1'a'Count of such string is: (n/1)=n

One

'b'can be placed at any of n positions, that's why n number of such strings'b', one'c'and (n-2)'a'Count of such string (n/2)*2=n*(n-1)

One

'b'and one'c'can take any of two places out of n and any of'b'&'c'can comes first.'b', two'c'and (n-3)'a'Count of such string (n/3)*3=n*(n-1)*(n-2)/2

One

'b'and two'c'can take any of three places out of n and there are 3 combinations possible between one'b'& two'c'.'c'and (n-2)'a'Count of such string (n/2)=n*(n-1)/2

Two

'c'can take any two of n places.'c'and (n-1)'a'Count of such string (n/1)=n

One

'c'can take any of one places out of n.Example with explanationC++ implementation

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