Ivan Arxont

var persons = new[]
{
    new { Name = "Юрий Васильевич Кондратюк",    BirthDate = new DateTime(1897, 06,  9) },
    new { Name = "Михаил Фёдорович Решетнёв",    BirthDate = new DateTime(1924, 11, 10) },
    new { Name = "Михаил Тимофеевич Калашников", BirthDate = new DateTime(1919, 11, 10) },
    new { Name = "Сергей Павлович Королёв",      BirthDate = new DateTime(1907,  1, 12) },
    new { Name = "Михаил Васильевич Ломоносов",  BirthDate = new DateTime(1711, 11,  8) }
};

int[] arr = persons.Where(n => n.Name.Contains("Михаил"))
                   .GroupBy(day => day.BirthDate.Day)
                   .Select(count => count.Count())
                   .ToArray();        

Array.ForEach(arr, Console.WriteLine);